Movatterモバイル変換


[0]ホーム

URL:


DLMF
About the Project

Software Index

Software Cross IndexA Classification of SoftwareSoftware Repositories

Software Cross Index

Open SourceWith BookCommercial
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
LanguageCInt.CFtnCC++CInt.C#Int. CFtnInt.PyCC JavaC C++ FtnC Ftn MmaFtnFtnC Ftn JavaInt.Int.Int.C Ftn
4Elementary Functions
4.48(ii)Interval ArithmeticaCoStLy
4.48(iii)General PrecisionaREDUCE
4.48(iv)LambertW-Functiona
4.48(v)Testing
5Gamma Function
5.24(ii)Γ(x),xFDLIBM
5.24(iii)ψ(x),ψ(n)(x),x
5.24(iv)Γ(z),ψ(z),ψ(n)(z),z
5.24(v)B(a,b),a,b
5.24(vi)B(a,b),a,baa
6Exponential, Logarithmic, Sine, andCosine Integrals
6.21(ii)E1(x),Ei(x),Si(x),Ci(x),Shi(x),Chi(x),x
6.21(iii)E1(z),Si(z),Ci(z),Shi(z),Chi(z),z
7Error Functions, Dawson’s and Fresnel Integrals
7.25(ii)erfx,erfcx,inerfc(x),xNMS
7.25(iii)erfz,erfcz,w(z),za
7.25(iv)C(x),S(x),f(x),g(x),xa
7.25(v)C(z),S(z),za
7.25(vi)(x),G(x),𝖴(x,t),𝖵(x,t),x
7.25(vii)(z),G(z),z
8Incomplete Gamma and RelatedFunctions
8.28(ii)γ(a,x),Γ(a,x),γ(a,x),P(a,x),Q(a,x),x,a
8.28(iii)γ(a,x),Γ(a,x),γ(a,x),P(a,x),Q(a,x),x,a
8.28(iv)Bx(a,b),Ix(a,b),x,a,b
8.28(v)Bz(a,b),Iz(a,b),z,a,ba
8.28(vi)Ep(x),x,p
8.28(vii)Ep(z),z,p
9Airy and Related Functions
9.20(ii)Ai(x),Ai(x),Bi(x),Bi(x),x
9.20(iii)Ai(z),Ai(z),Bi(z),Bi(z),za
9.20(iv)Zeros of …aa
9.20(v)Integrals of …aa
9.20(vi)Scorer Functionsa
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 ArgumentNMS
10.77(iv)Bessel Functions–Integer or Half-Integer Order and ComplexArguments, including Kelvin Functionsa
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 Functionsaa
10.77(x)Zeros of Bessel Functionsaa
11Struve and Related Functions
11.16(ii)𝐇ν(z),𝐊ν(z)aa
11.16(iii)Integrals of …a
11.16(iv)sμ,ν(z),Sμ,ν(z)aa
11.16(v)𝐉ν(z),𝐄ν(z),𝐀ν(z)aa
11.16(vi)Integrals of …a
12Parabolic Cylinder Functions
12.21(ii)U(a,x),V(a,x),U¯(a,x),W(a,x),x,aaa
12.21(iii)U(a,z),V(a,z),U¯(a,z),W(a,z),z,aaa
13Confluent Hypergeometric Functions
13.32(ii)M(a,b,x),U(a,b,x),𝐌(a,b,x),Mκ,μ(x),Wκ,μ(x),x,a,ba
13.32(iii)M(a,b,z),U(a,b,z),𝐌(a,b,z),Mκ,μ(z),Wκ,μ(z),z,a,ba
14Legendre and Related Functions
14.34(ii)𝖯ν(x),𝖰ν(x),Pν(x),Qν(x),x,νa
14.34(iii)𝖯ν(z),𝖰ν(z),Pν(z),Qν(z),z,νaa
14.34(iv)𝖯12+iτ(x),𝖰12+iτ(x),𝖰^12+iτμ(x),P12+iτ(x),Q12+iτ(x)
15Hypergeometric Function
15.20(ii)F12(a,b;c;x),x,a,b,caa
15.20(iii)F12(a,b;c;z),z,a,b,caa
16Generalized Hypergeometric Functions & MeijerG-Function
16.27(ii)Real Argumentsa
16.27(iii)Complex Argumentsa
18Orthogonal Polynomials
18.42SoftwareaKoornwinder,Stembridge
19Elliptic Integrals
19.39(ii)K(k),E(k),0k21
19.39(iii)F(ϕ,k),E(ϕ,k),ϕ,ka
19.39(iv)RC(x,y),RF(x,y,z),RD(x,y,z),RJ(x,y,z,p)aDerive
20Theta Functions
20.16(ii)Real argumentsaa
20.16(iii)Complex argumentsaa
21Multidimensional Theta Functions
21.11SoftwareaJTEM
22Jacobian Elliptic Functions
22.22(ii)Real Argument
22.22(iii)Complex Argumenta
23Weierstrass Elliptic and ModularFunctions
23.24(ii)Real Argumenta
23.24(iii)Complex Argumenta
24Bernoulli and Euler Polynomials
24.21(ii)Bn,Bn(x),En,En(x)aDerive,MuPAD
25Zeta and Related Functions
25.21(ii)ζ(s),s
25.21(iii)ζ(s),s
25.21(iv)ζ(s,a)a
25.21(v)Li2(z),Lis(z)
25.21(vi)Clausen’s IntegralaNetNUMPAC
25.21(vii)Fermi–Dirac, Bose–Einstein
25.21(viii)Lerch’s Transcendentaa
25.21(ix)DirichletL-seriesa
26Combinatorial Analysis
26.22SoftwareaWolfram’s Mathworld,Zeilberger
27Functions of Number Theory
27.22Softwarea
28Mathieu Functions and Hill’s Equation
28.36(ii)Exponents, Eigenvaluesa
28.36(iii)Mathieu FunctionsaVan Buren
30Spheroidal Wave Functions
30.18(ii)Eigenvaluesλnm(γ2)
30.18(iii)Wave FunctionsVan Buren
33Coulomb Functions
33.26(ii)Real argumentsaa
33.26(iii)Complex argumentsa
343j, 6j, 9j Symbols
34.15Softwarea
35Functions of Matrix Argument
35.12SoftwareZeilberger

‘✓’ 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.

© 2010–2025 NIST /Disclaimer /Feedback; Version 1.2.4;Release date 2025-03-15.
NIST
Site PrivacyAccessibilityPrivacy ProgramCopyrightsVulnerability DisclosureNo Fear Act PolicyFOIAEnvironmental PolicyScientific IntegrityInformation Quality StandardsCommerce.govScience.govUSA.gov

[8]ページ先頭

©2009-2025 Movatter.jp