diff --git a/changelog b/changelog index 37c11ce..5d27d71 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,6 @@ +20100620 tpd src/axiom-website/patches.html 20100620.04.tpd.patch +20100620 tpd src/input/Makefile integral function integration +20100620 tpd src/input/richspecfunc000-022.input special function integration 20100620 tpd src/axiom-website/patches.html 20100620.03.tpd.patch 20100620 tpd src/input/Makefile integral function integration 20100620 tpd src/input/richintfunc000-032.input integral function integration diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index fe405de..8324fcd 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2932,6 +2932,8 @@ src/input/richinvhyper200-296.input inverse hyperbolic int.
src/input/richerror000-078.input error function integration
20100620.03.tpd.patch src/input/richintfunc000-032.input integral function integration
+20100620.04.tpd.patch +src/input/richspecfunc000-022.input special function integration
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 59ef11e..32c011b 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -397,6 +397,7 @@ REGRES= ackermann.regress \ richlog200-299.regress \ richlog300-391.regress \ richrational.regress \ + richspecfunc000-022.regress \ richtrig000-099.regress \ richtrig100-199.regress \ richtrig200-299.regress \ @@ -747,6 +748,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/richlog200-299.input \ ${OUT}/richlog300-391.input \ ${OUT}/richrational.input \ + ${OUT}/richspecfunc000-022.input \ ${OUT}/richtrig000-099.input \ ${OUT}/richtrig100-199.input \ ${OUT}/richtrig200-299.input \ @@ -1126,6 +1128,7 @@ DOCFILES= \ ${DOC}/richlog200-299.input.dvi \ ${DOC}/richlog300-391.input.dvi \ ${DOC}/richrational.input.dvi \ + ${DOC}/richspecfunc000-022.input.dvi \ ${DOC}/richtrig000-099.input.dvi \ ${DOC}/richtrig100-199.input.dvi \ ${DOC}/richtrig200-299.input.dvi \ diff --git a/src/input/richspecfunc000-022.input.pamphlet b/src/input/richspecfunc000-022.input.pamphlet new file mode 100644 index 0000000..1856ef8 --- /dev/null +++ b/src/input/richspecfunc000-022.input.pamphlet @@ -0,0 +1,1118 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input richspecfunc000-022.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richspecfunc000-022.output +)spool richspecfunc000-022.output +)set message auto off +)clear all + +--S 1 of 115 +t0000:= Gamma(n,a+b*x) +--R +--R +--R _ +--R (1) | (n,b x + a) +--R Type: Expression Integer +--E 1 + +--S 2 of 115 +r0000:= (a+b*x)*Gamma(n,a+b*x)/b-Gamma(1+n,a+b*x)/b +--R +--R +--R _ _ +--R - | (n + 1,b x + a) + (b x + a)| (n,b x + a) +--R (2) -------------------------------------------- +--R b +--R Type: Expression Integer +--E 2 + +--S 3 of 115 +a0000:= integrate(t0000,x) +--R +--R +--R x +--R ++ _ +--R (3) | | (n,%K b + a)d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 115 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 115 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 115 +t0001:= x*Gamma(n,a+b*x) +--R +--R +--R _ +--R (4) x| (n,b x + a) +--R Type: Expression Integer +--E 6 + +--S 7 of 115 +r0001:= -1/2*(a^2/b^2-x^2)*Gamma(n,a+b*x)+a*Gamma(1+n,a+b*x)/b^2-1/2*_ + Gamma(2+n,a+b*x)/b^2 +--R +--R +--R _ _ 2 2 2 _ +--R - | (n + 2,b x + a) + 2a| (n + 1,b x + a) + (b x - a )| (n,b x + a) +--R (5) -------------------------------------------------------------------- +--R 2 +--R 2b +--R Type: Expression Integer +--E 7 + +--S 8 of 115 +a0001:= integrate(t0001,x) +--R +--R +--R x +--R ++ _ +--R (6) | %K| (n,%K b + a)d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 115 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 115 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 115 +t0002:= x^2*Gamma(n,a+b*x) +--R +--R +--R 2 _ +--R (7) x | (n,b x + a) +--R Type: Expression Integer +--E 11 + +--S 12 of 115 +r0002:= -1/3*(-Gamma(n,a+b*x)*a^3-Gamma(n,a+b*x)*b^3*x^3+3*a^2*_ + Gamma(1+n,a+b*x)-3*a*Gamma(2+n,a+b*x)+Gamma(3+n,a+b*x))/b^3 +--R +--R +--R (8) +--R _ _ 2 _ +--R - | (n + 3,b x + a) + 3a| (n + 2,b x + a) - 3a | (n + 1,b x + a) +--R + +--R 3 3 3 _ +--R (b x + a )| (n,b x + a) +--R / +--R 3 +--R 3b +--R Type: Expression Integer +--E 12 + +--S 13 of 115 +a0002:= integrate(t0002,x) +--R +--R +--R x +--R ++ 2 _ +--R (9) | %K | (n,%K b + a)d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 115 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 115 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 115 +t0003:= log(Gamma(a+b*x)) +--R +--R +--R _ +--R (10) log(| (b x + a)) +--R Type: Expression Integer +--E 16 + +--S 17 of 115 +r0003:= x*log(Gamma(a+b*x))-x*logGamma(a+b*x)+Psi(-2,a+b*x)/b +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 115 +a0003:= integrate(t0003,x) +--R +--R +--R x +--R ++ _ +--R (11) | log(| (%K b + a))d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 115 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 115 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 115 +t0004:= x*log(Gamma(a+b*x)) +--R +--R +--R _ +--R (12) x log(| (b x + a)) +--R Type: Expression Integer +--E 21 + +--S 22 of 115 +r0004:= 1/2*x^2*log(Gamma(a+b*x))-1/2*x^2*logGamma(a+b*x)-_ + Psi(-3,a+b*x)/b^2+x*Psi(-2,a+b*x)/b +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 115 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ _ +--R (13) | %K log(| (%K b + a))d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 115 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 115 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 115 +t0005:= x^2*log(Gamma(a+b*x)) +--R +--R +--R 2 _ +--R (14) x log(| (b x + a)) +--R Type: Expression Integer +--E 26 + +--S 27 of 115 +r0005:= 1/3*x^3*log(Gamma(a+b*x))-1/3*x^3*logGamma(a+b*x)+2*_ + Psi(-4,a+b*x)/b^3-2*x*Psi(-3,a+b*x)/b^2+x^2*Psi(-2,a+b*x)/b +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 115 +a0005:= integrate(t0005,x) +--R +--R +--R x +--R ++ 2 _ +--R (15) | %K log(| (%K b + a))d%K +--R ++ +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 115 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 115 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 115 +t0006:= logGamma(a+b*x) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 31 + +--S 32 of 115 +r0006:= Psi(-2,a+b*x)/b +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 115 +--a0006:= integrate(t0006,x) +--E 33 + +--S 34 of 115 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 115 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 115 +t0007:= x*logGamma(a+b*x) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 36 + +--S 37 of 115 +r0007:= -(Psi(-3,a+b*x)-x*Psi(-2,a+b*x)*b)/b^2 +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 115 +--a0007:= integrate(t0007,x) +--E 38 + +--S 39 of 115 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 115 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 115 +t0008:= x^2*logGamma(a+b*x) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 41 + +--S 42 of 115 +r0008:= 2*Psi(-4,a+b*x)/b^3-2*x*Psi(-3,a+b*x)/b^2+x^2*Psi(-2,a+b*x)/b +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 115 +--a0008:= integrate(t0008,x) +--E 43 + +--S 44 of 115 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 115 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 115 +t0009:= x*Psi(n,a+b*x) +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Variable n +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 46 + +--S 47 of 115 +r0009:= (-Psi(-2+n,a+b*x)+x*Psi(-1+n,a+b*x)*b)/b^2 +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Polynomial Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 115 +--a0009:= integrate(t0009,x) +--E 48 + +--S 49 of 115 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 115 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 115 +t0010:= x^2*Psi(1,a+b*x) +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 51 + +--S 52 of 115 +r0010:= (-2*x*logGamma(a+b*x)*b+2*Psi(-2,a+b*x)+x^2*Psi(a+b*x)*b^2)/b^3 +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 115 +--a0010:= integrate(t0010,x) +--E 53 + +--S 54 of 115 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 115 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 115 +t0011:= x*Zeta(2,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 56 + +--S 57 of 115 +r0011:= (-logGamma(a+b*x)+x*Psi(a+b*x)*b)/b^2 +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 115 +--a0011:= integrate(t0011,x) +--E 58 + +--S 59 of 115 +--m0011:= a0011-r0011 +--E 59 + +--S 60 of 115 +--d0011:= D(m0011,x) +--E 60 + +--S 61 of 115 +t0012:= x^2*Zeta(2,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 61 + +--S 62 of 115 +r0012:= (-2*x*logGamma(a+b*x)*b+2*Psi(-2,a+b*x)+x^2*Psi(a+b*x)*b^2)/b^3 +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 115 +--a0012:= integrate(t0012,x) +--E 63 + +--S 64 of 115 +--m0012:= a0012-r0012 +--E 64 + +--S 65 of 115 +--d0012:= D(m0012,x) +--E 65 + +--S 66 of 115 +t0013:= Zeta(s,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Variable s +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 66 + +--S 67 of 115 +r0013:= -Zeta(-1+s,a+b*x)/b/(-1+s) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Polynomial Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 115 +--a0013:= integrate(t0013,x) +--E 68 + +--S 69 of 115 +--m0013:= a0013-r0013 +--E 69 + +--S 70 of 115 +--d0013:= D(m0013,x) +--E 70 + +--S 71 of 115 +t0014:= x*Zeta(s,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Variable s +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 71 + +--S 72 of 115 +r0014:= -Zeta(-2+s,a+b*x)/b^2/(1-s)/(2-s)+x*Zeta(-1+s,a+b*x)/b/(1-s) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Polynomial Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 115 +--a0014:= integrate(t0014,x) +--E 73 + +--S 74 of 115 +--m0014:= a0014-r0014 +--E 74 + +--S 75 of 115 +--d0014:= D(m0014,x) +--E 75 + +--S 76 of 115 +t0015:= x^2*Zeta(s,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Variable s +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 76 + +--S 77 of 115 +r0015:= 2*Zeta(-3+s,a+b*x)/b^3/(1-s)/(2-s)/(3-s)-_ + 2*x*Zeta(-2+s,a+b*x)/b^2/(1-s)/(2-s)+x^2*Zeta(-1+s,a+b*x)/b/(1-s) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Polynomial Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 115 +--a0015:= integrate(t0015,x) +--E 78 + +--S 79 of 115 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 115 +--d0015:= D(m0015,x) +--E 80 + +--S 81 of 115 +t0016:= polylog(n,a*x^m)/x +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable n +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 115 +r0016:= polylog(1+n,a*x^m)/m +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial Integer +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 115 +--a0016:= integrate(t0016,x) +--E 83 + +--S 84 of 115 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 115 +--d0016:= D(m0016,x) +--E 85 + +--S 86 of 115 +t0017:= polylog(2,a+b*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 86 + +--S 87 of 115 +r0017:= -x-(1-a-b*x)*log(1-a-b*x)/b+(x+a/b)*polylog(2,a+b*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 115 +--a0017:= integrate(t0017,x) +--E 88 + +--S 89 of 115 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 115 +--d0017:= D(m0017,x) +--E 90 + +--S 91 of 115 +t0018:= polylog(n,a*f^x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable n +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 91 + +--S 92 of 115 +r0018:= polylog(1+n,a*f^x)/log(f) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial Integer +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 115 +--a0018:= integrate(t0018,x) +--E 93 + +--S 94 of 115 +--m0018:= a0018-r0018 +--E 94 + +--S 95 of 115 +--d0018:= D(m0018,x) +--E 95 + +--S 96 of 115 +t0019:= x*polylog(n,a*f^x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable n +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 96 + +--S 97 of 115 +r0019:= 1/log(f)^2*(x*polylog(1+n,a*f^x)*log(f)-polylog(2+n,a*f^x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial Integer +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 115 +--a0019:= integrate(t0019,x) +--E 98 + +--S 99 of 115 +--m0019:= a0019-r0019 +--E 99 + +--S 100 of 115 +--d0019:= D(m0019,x) +--E 100 + +--S 101 of 115 +t0020:= x^2*polylog(n,a*f^x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable n +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 101 + +--S 102 of 115 +r0020:= 1/log(f)^3*(x^2*polylog(1+n,a*f^x)*log(f)^2-_ + 2*x*polylog(2+n,a*f^x)*log(f)+2*polylog(3+n,a*f^x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial Integer +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 115 +--a0020:= integrate(t0020,x) +--E 103 + +--S 104 of 115 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 115 +--d0020:= D(m0020,x) +--E 105 + +--S 106 of 115 +t0021:= log(x)*polylog(n,a*x)/x +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable n +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 106 + +--S 107 of 115 +r0021:= log(x)*polylog(1+n,a*x)-polylog(2+n,a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 115 +--a0021:= integrate(t0021,x) +--E 108 + +--S 109 of 115 +--m0021:= a0021-r0021 +--E 109 + +--S 110 of 115 +--d0021:= D(m0021,x) +--E 110 + +--S 111 of 115 +t0022:= log(x)^2*polylog(n,a*x)/x +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable n +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 111 + +--S 112 of 115 +r0022:= log(x)^2*polylog(1+n,a*x)-2*log(x)*polylog(2+n,a*x)+2*polylog(3+n,a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial Integer +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 115 +--a0022:= integrate(t0022,x) +--E 113 + +--S 114 of 115 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 115 +--d0022:= D(m0022,x) +--E 115 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document}