Software Index

♦Software Cross Index ♦A Classification of Software ♦Software Repositories ♦

Software Cross Index

\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Arblib\hfil}}}}

\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Axiom\hfil}}}}

‘✓’ indicates that a software package implements the functions in a section;‘a’ indicates available functionality through optional or add-on packages;an empty space indicates no known support.

A Classification of Software

In the list below we identify four main sources of software for computing special functions.Please see ourSoftware Indexing Policy for rules that govern the indexing ofsoftware in the DLMF.

Research Software.: This is software of narrow scope developed as a byproductof a research project and subsequently made available at no cost to the public.The software is often meant to demonstrate new numerical methods or softwareengineering strategies which were the subject of a research project. Whendeveloped, the software typically contains capabilities unavailable elsewhere.While the software may be quite capable, it is typically not professionallypackaged and its use may require some expertise. The software is typicallyprovided as source code or via a web-based service, and no support is provided.
Open Source Collections and Systems.: These are collections of software (e.g. libraries) or interactive systems ofa somewhat broad scope. Contents may be adapted from research software or maybe contributed by project participants who donate their services to the project.The software is made freely available to the public, typically in source code form.While formal support of the collection may not be provided by its developers,within active projects there is often a core group whodonate time to consider bug reports and make updates to the collection.
Software Associated with Books.: An increasing number of published books haveincluded digital media containing software described in the book. Often, thecollection of software covers a fairly broad area. Such software is typicallydeveloped by the book author. While it is not professionally packaged,it often provides a useful tool for readers to experiment with the conceptsdiscussed in the book. The software itself is typically not formally supportedby its authors.
Commercial Software.: Such software ranges from a collection of reusable softwareparts (e.g., a library) to fully functional interactive computing environmentswith an associated computing language. Such software is usually professionallydeveloped, tested, and maintained to high standards. It is available for purchase,often with accompanying updates and consulting support.

Software Repositories

The following are web-based software repositories with significant holdings in thearea of special functions. Many research software packages are found here, as wellas some open source software collections.

Collected Algorithms of the ACM: Software published by the journal ACMTransactions on Mathematical Software(TOMS).
Computer Physics Communications Program Library: Software associated with papers published in the journalComputer PhysicsCommunications.
netlib: A collection of mathematical software, papers, and databases produced bythe numerical analysis research community.
Guide to Available Mathematical Software: A cross index of mathematical software in use at NIST.

List of Tables Errata

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov

	Open Source													With Book						Commercial
Package	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Arblib\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Axiom\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}CEPHES\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}FN\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}GSL\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Kormanyos\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}MPFR\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Maxima\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Meta.Numerics\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}PARI-GP\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}SLATEC\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Sage\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}mpmath\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Baker\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Lau\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Num.~{}Recipes\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Thompson\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Watanabe\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Zhang\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}IMSL\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Maple\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Mathematica\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col0}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}Matlab\hfil}}}}$	$\definecolor{col0}{rgb}{0.81,1.0,0.81}\definecolor{col1}{rgb}{0.94,1.0,0.94}\rotatebox{90.0}{\hbox{\pagecolor{col1}{\color[rgb]{0,0,1}\hbox to75.0001pt{~{%}NAG\hfil}}}}$	See Also
Language	C	Int.	C	Ftn	C	C++	C	Int.	C $\#$	Int. C	Ftn	Int.	Py	C	C Java	C C++ Ftn	C Ftn Mma	Ftn	Ftn	C Ftn Java	Int.	Int.	Int.	C Ftn
4Elementary Functions
4.48(ii)Interval Arithmetic	✓					✓						✓	✓								✓	✓	a		CoStLy
4.48(iii)General Precision	✓					✓	✓	✓				✓	✓								✓	✓	a		REDUCE
4.48(iv)Lambert $W$ -Function	✓					✓			✓			✓	✓								✓	✓	a
4.48(v)Testing
5Gamma Function
5.24(ii) $\Gamma\left(x\right)$ , $x\in\mathbb{R}$	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	FDLIBM
5.24(iii) $\psi\left(x\right)$ , $\psi^{(n)}\left(x\right)$ , $x\in\mathbb{R}$	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓	✓			✓		✓	✓	✓	✓	✓	✓
5.24(iv) $\Gamma\left(z\right)$ , $\psi\left(z\right)$ , $\psi^{(n)}\left(z\right)$ , $z\in\mathbb{C}$	✓	✓		✓		✓			✓	✓	✓	✓	✓	✓				✓	✓	✓	✓	✓	✓	✓
5.24(v) $\mathrm{B}\left(a,b\right)$ , $a,b\in\mathbb{R}$	✓	✓	✓	✓	✓	✓		✓	✓		✓	✓	✓	✓			✓		✓	✓	✓	✓	✓
5.24(vi) $\mathrm{B}\left(a,b\right)$ , $a,b\in\mathbb{C}$	✓	✓		✓							✓	a	✓							✓	✓	✓	a
6Exponential, Logarithmic, Sine, andCosine Integrals
6.21(ii) $E_{1}\left(x\right)$ , $\operatorname{Ei}\left(x\right)$ , $\operatorname{Si}\left(x\right)$ , $\operatorname{Ci}\left(x\right)$ , $\operatorname{Shi}\left(x\right)$ , $\operatorname{Chi}\left(x\right)$ , $x\in\mathbb{R}$	✓	✓	✓	✓	✓	✓	✓		✓		✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
6.21(iii) $E_{1}\left(z\right)$ , $\operatorname{Si}\left(z\right)$ , $\operatorname{Ci}\left(z\right)$ , $\operatorname{Shi}\left(z\right)$ , $\operatorname{Chi}\left(z\right)$ , $z\in\mathbb{C}$	✓	✓				✓			✓			✓	✓	✓							✓	✓	✓
7Error Functions, Dawson’s and Fresnel Integrals
7.25(ii) $\operatorname{erf}x$ , $\operatorname{erfc}x$ , $\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(x\right)$ , $x\in\mathbb{R}$	✓		✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓	NMS
7.25(iii) $\operatorname{erf}z$ , $\operatorname{erfc}z$ , $w\left(z\right)$ , $z\in\mathbb{C}$	✓								✓			a	✓	✓							✓	✓	✓
7.25(iv) $C\left(x\right)$ , $S\left(x\right)$ , $\mathrm{f}\left(x\right)$ , $\mathrm{g}\left(x\right)$ , $x\in\mathbb{R}$	✓		✓						✓			a	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
7.25(v) $C\left(z\right)$ , $S\left(z\right)$ , $z\in\mathbb{C}$	✓											a	✓								✓	✓	✓
7.25(vi) $\mathcal{F}\left(x\right)$ , $G\left(x\right)$ , $\mathsf{U}\left(x,t\right)$ , $\mathsf{V}\left(x,t\right)$ , $x\in\mathbb{R}$			✓	✓	✓						✓			✓	✓	✓	✓			✓	✓	✓	✓
7.25(vii) $\mathcal{F}\left(z\right)$ , $G\left(z\right)$ , $z\in\mathbb{C}$																					✓	✓	✓
8Incomplete Gamma and RelatedFunctions
8.28(ii) $\gamma\left(a,x\right)$ , $\Gamma\left(a,x\right)$ , $\gamma^{*}\left(a,x\right)$ , $P\left(a,x\right)$ , $Q\left(a,x\right)$ , $x,a\in\mathbb{R}$	✓		✓	✓	✓	✓			✓		✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓
8.28(iii) $\gamma\left(a,x\right)$ , $\Gamma\left(a,x\right)$ , $\gamma^{*}\left(a,x\right)$ , $P\left(a,x\right)$ , $Q\left(a,x\right)$ , $x,a\in\mathbb{C}$	✓		✓	✓	✓						✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓	✓	✓
8.28(iv) $\mathrm{B}_{x}\left(a,b\right)$ , $I_{x}\left(a,b\right)$ , $x,a,b\in\mathbb{R}$	✓								✓
8.28(v) $\mathrm{B}_{z}\left(a,b\right)$ , $I_{z}\left(a,b\right)$ , $z,a,b\in\mathbb{C}$	✓											a	✓									✓
8.28(vi) $E_{p}\left(x\right)$ , $x\in\mathbb{R}$ , $p\in\mathbb{Z}$	✓		✓		✓				✓		✓	✓	✓	✓	✓	✓			✓	✓	✓	✓	✓
8.28(vii) $E_{p}\left(z\right)$ , $z,p\in\mathbb{C}$	✓											✓	✓								✓	✓	✓
9Airy and Related Functions
9.20(ii) $\operatorname{Ai}\left(x\right)$ , $\operatorname{Ai}'\left(x\right)$ , $\operatorname{Bi}\left(x\right)$ , $\operatorname{Bi}'\left(x\right)$ , $x\in\mathbb{R}$	✓	✓	✓	✓	✓	✓		✓	✓		✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓
9.20(iii) $\operatorname{Ai}\left(z\right)$ , $\operatorname{Ai}'\left(z\right)$ , $\operatorname{Bi}\left(z\right)$ , $\operatorname{Bi}'\left(z\right)$ , $z\in\mathbb{C}$	✓	✓						✓			✓	a	✓	✓							✓	✓	✓	✓
9.20(iv)Zeros of …	✓				✓							a	✓								✓	✓	a
9.20(v)Integrals of …	✓											a	✓	✓					✓		✓	✓	a
9.20(vi)Scorer Functions	✓											a	✓
10Bessel Functions
10.77(ii)Bessel Functions–Real Argument and Integer or Half-Integer Order(including Spherical Bessel Functions)	✓	✓	✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	FDLIBM,NMS
10.77(iii)Bessel Functions–Real Order and Argument	✓	✓	✓	✓	✓	✓		✓	✓		✓	✓	✓		✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	NMS
10.77(iv)Bessel Functions–Integer or Half-Integer Order and ComplexArguments, including Kelvin Functions	✓	✓	✓									a	✓	✓			✓	✓	✓	✓	✓	✓	✓
10.77(v)Bessel Functions–Real Order and Complex Argument (includingHankel Functions)	✓	✓									✓	a	✓						✓	✓	✓	✓	✓
10.77(vi)Bessel Functions–Imaginary Order and Real Argument	✓	✓										✓	✓								✓	✓	✓
10.77(viii)Bessel Functions–Complex Order and Argument	✓	✓										✓	✓								✓	✓	✓
10.77(ix)Integrals of Bessel Functions	✓										✓	a	✓	✓					✓		✓	✓	a
10.77(x)Zeros of Bessel Functions					✓							a	✓	✓	✓				✓		✓	✓	a
11Struve and Related Functions
11.16(ii) $\mathbf{H}_{\nu}\left(z\right)$ , $\mathbf{K}_{\nu}\left(z\right)$			✓									a	✓	✓			✓		✓		✓	✓	a
11.16(iii)Integrals of …														✓					✓		✓	✓	a
11.16(iv) $s_{{\mu},{\nu}}\left(z\right)$ , $S_{{\mu},{\nu}}\left(z\right)$												a	✓				✓				✓		a
11.16(v) $\mathbf{J}_{\nu}\left(z\right)$ , $\mathbf{E}_{\nu}\left(z\right)$ , $\mathbf{A}_{\nu}\left(z\right)$												a	✓				✓				✓	✓	a
11.16(vi)Integrals of …														✓							✓	✓	a
12Parabolic Cylinder Functions
12.21(ii) $U\left(a,x\right)$ , $V\left(a,x\right)$ , $\overline{U}\left(a,x\right)$ , $W\left(a,x\right)$ , $x,a\in\mathbb{R}$						✓						a	✓				✓		✓		✓	✓	a
12.21(iii) $U\left(a,z\right)$ , $V\left(a,z\right)$ , $\overline{U}\left(a,z\right)$ , $W\left(a,z\right)$ , $z,a\in\mathbb{C}$												a	✓								✓	✓	a
13Confluent Hypergeometric Functions
13.32(ii) $M\left(a,b,x\right)$ , $U\left(a,b,x\right)$ , ${\mathbf{M}}\left(a,b,x\right)$ , $M_{\kappa,\mu}\left(x\right)$ , $W_{\kappa,\mu}\left(x\right)$ , $x,a,b\in\mathbb{R}$	✓		✓	✓	✓	✓						✓	✓	✓			✓		✓		✓	✓	a
13.32(iii) $M\left(a,b,z\right)$ , $U\left(a,b,z\right)$ , ${\mathbf{M}}\left(a,b,z\right)$ , $M_{\kappa,\mu}\left(z\right)$ , $W_{\kappa,\mu}\left(z\right)$ , $z,a,b\in\mathbb{C}$	✓											✓	✓	✓					✓		✓	✓	a
14Legendre and Related Functions
14.34(ii) $\mathsf{P}_{\nu}\left(x\right)$ , $\mathsf{Q}_{\nu}\left(x\right)$ , $P_{\nu}\left(x\right)$ , $Q_{\nu}\left(x\right)$ , $x,\nu\in\mathbb{R}$	✓				✓	✓					✓	a	✓	✓		✓	✓		✓		✓	✓	✓	✓
14.34(iii) $\mathsf{P}_{\nu}\left(z\right)$ , $\mathsf{Q}_{\nu}\left(z\right)$ , $P_{\nu}\left(z\right)$ , $Q_{\nu}\left(z\right)$ , $z,\nu\in\mathbb{C}$	✓											a	✓	✓							✓	✓	a
14.34(iv) $\mathsf{P}_{-\frac{1}{2}+i\tau}\left(x\right)$ , $\mathsf{Q}_{-\frac{1}{2}+i\tau}\left(x\right)$ , $\widehat{\mathsf{Q}}^{\mu}_{-\frac{1}{2}+i\tau}\left(x\right)$ , $P_{-\frac{1}{2}+i\tau}\left(x\right)$ , $Q_{-\frac{1}{2}+i\tau}\left(x\right)$					✓									✓			✓
15Hypergeometric Function
15.20(ii) ${{}_{2}F_{1}}\left(a,b;c;x\right)$ , $x,a,b,c\in\mathbb{R}$	✓		✓		✓	✓						a	✓	✓			✓		✓		✓	✓	a
15.20(iii) ${{}_{2}F_{1}}\left(a,b;c;z\right)$ , $z,a,b,c\in\mathbb{C}$	✓											a	✓			✓					✓	✓	a
16Generalized Hypergeometric Functions & MeijerG-Function
16.27(ii)Real Arguments	✓		✓		✓	✓						a	✓								✓	✓	✓
16.27(iii)Complex Arguments	✓											a	✓								✓	✓	✓
18Orthogonal Polynomials
18.42Software	✓	✓				✓			✓			✓	✓								✓	✓	a		Koornwinder,Stembridge
19Elliptic Integrals
19.39(ii) $K\left(k\right)$ , $E\left(k\right)$ , $0\leq k^{2}\leq 1$	✓		✓		✓	✓		✓	✓			✓	✓							✓	✓	✓	✓
19.39(iii) $F\left(\phi,k\right)$ , $E\left(\phi,k\right)$ , $\phi,k\in\mathbb{R}$	✓		✓		✓	✓		✓	✓			✓	✓			✓					✓	✓	a	✓
19.39(iv) $R_{C}\left(x,y\right)$ , $R_{F}\left(x,y,z\right)$ , $R_{D}\left(x,y,z\right)$ , $R_{J}\left(x,y,z,p\right)$	✓				✓				✓		✓	a	✓			✓				✓				✓	Derive
20Theta Functions
20.16(ii)Real arguments	✓											a	✓	✓			✓				✓	✓	a	✓
20.16(iii)Complex arguments	✓											a	✓	✓							✓	✓	a
21Multidimensional Theta Functions
21.11Software																					✓	✓	a		JTEM
22Jacobian Elliptic Functions
22.22(ii)Real Argument	✓		✓		✓	✓		✓				✓	✓	✓		✓	✓		✓	✓	✓	✓	✓	✓
22.22(iii)Complex Argument	✓					✓						✓	✓	✓						✓	✓	✓	a	✓
23Weierstrass Elliptic and ModularFunctions
23.24(ii)Real Argument																					✓	✓	a
23.24(iii)Complex Argument														✓						✓	✓	✓	a
24Bernoulli and Euler Polynomials
24.21(ii) $B_{n}$ , $B_{n}\left(x\right)$ , $E_{n}$ , $E_{n}\left(x\right)$	✓	✓						✓		✓		a	✓	✓			✓		✓		✓	✓	✓		Derive,MuPAD
25Zeta and Related Functions
25.21(ii) $\zeta\left(s\right)$ , $s\in\mathbb{R}$	✓		✓		✓	✓	✓	✓	✓			✓	✓	✓			✓				✓	✓	✓
25.21(iii) $\zeta\left(s\right)$ , $s\in\mathbb{C}$	✓					✓			✓			✓	✓	✓							✓	✓	✓
25.21(iv) $\zeta\left(s,a\right)$	✓				✓	✓						✓	✓	✓			✓				✓	✓	a
25.21(v) $\operatorname{Li}_{2}\left(z\right)$ , $\operatorname{Li}_{s}\left(z\right)$	✓		✓		✓	✓	✓		✓			✓	✓	✓			✓				✓	✓	✓
25.21(vi)Clausen’s Integral					✓				✓			a	✓									✓			NetNUMPAC
25.21(vii)Fermi–Dirac, Bose–Einstein					✓									✓			✓					✓
25.21(viii)Lerch’s Transcendent												a	✓								✓	✓	a
25.21(ix)Dirichlet $L$ -series	✓											a	✓									✓
26Combinatorial Analysis
26.22Software						✓						✓									✓	✓	a		Wolfram’s Mathworld,Zeilberger
27Functions of Number Theory
27.22Software	✓					✓				✓		✓									✓	✓	a
28Mathieu Functions and Hill’s Equation
28.36(ii)Exponents, Eigenvalues														✓					✓	✓	✓	✓	a
28.36(iii)Mathieu Functions														✓					✓	✓	✓	✓	a		Van Buren
30Spheroidal Wave Functions
30.18(ii)Eigenvalues $\lambda^{m}_{n}\left(\gamma^{2}\right)$														✓			✓		✓			✓
30.18(iii)Wave Functions														✓			✓		✓			✓			Van Buren
33Coulomb Functions
33.26(ii)Real arguments	✓				✓				✓			a	✓	✓			✓				✓		a
33.26(iii)Complex arguments	✓											a	✓
343j, 6j, 9j Symbols
34.15Software					✓	✓			✓		✓	✓		✓			✓				✓	✓	a
35Functions of Matrix Argument
35.12Software																									Zeilberger

Movatterモバイル変換

Software Index

Software Cross Index

A Classification of Software

Software Repositories