特殊関数 (Japanese Wikipedia)

Analysis of information sources in references of the Wikipedia article "特殊関数" in Japanese language version.

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10wikipedia.org

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ams.org

mathscinet.ams.org

Exton, Harold (1976), Multiple hypergeometric functions and applications, Mathematics and its applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-470-15190-7, MR0422713
Exton, Harold (1978), Handbook of hypergeometric integrals, Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-122-0, MR0474684
Exton, Harold (1983), q-hypergeometric functions and applications, Ellis Horwood Series: Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-491-7, MR708496

books.google.com

Exton, Harold (1976), Multiple hypergeometric functions and applications, Mathematics and its applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-470-15190-7, MR0422713
Exton, Harold (1978), Handbook of hypergeometric integrals, Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-122-0, MR0474684
Exton, Harold (1983), q-hypergeometric functions and applications, Ellis Horwood Series: Mathematics and its Applications, Chichester: Ellis Horwood Ltd., ISBN 978-0-85312-491-7, MR708496

cambridge.org

Ismail, Mourad E. H. (2005). Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge: en:Cambridge University Press. ISBN 0-521-78201-5

cybernet.co.jp

Mapleにある特殊関数の一覧

mathworks.com

jp.mathworks.com

MATLABにある特殊関数の一覧

researchmap.jp

ロシアでの微積分の用語、Researchmapより

uva.nl

staff.fnwi.uva.nl

Askey-Bateman project

wikipedia.org

en.wikipedia.org

Watson, G. N. (1995). A treatise on the theory of Bessel functions. en:Cambridge university press.
Ismail, Mourad E. H. (2005). Classical and Quantum Orthogonal Polynomials in One Variable. Cambridge: en:Cambridge University Press. ISBN 0-521-78201-5
Encyclopedia of Special Functions: The Askey–Bateman Project, Encyclopedia of Special Functions: The Askey–Bateman Project, Volume 1: Univariate Orthogonal Polynomials, Edited by Mourad E. H. Ismail, University of Central Florida, Published by en:Cambridge University Press, March 2020, ISBN 9780511979156.
例えばパンルヴェ方程式の厳密解はパンルヴェ超越関数 (en:Painleve transcendent) という特殊関数になる。
Gradshtein, Israel Solomonovich; Iosif Moiseevich Ryzhik.. Table of integrals, sums, series and products. en:Academic press
Olver, F. (1997). Asymptotics and special functions. AK Peters/CRC Press.
収束が遅いときには収束加速法を使うことで収束が早くなる場合がある。
Gasper and Rahman, Basic Hypergeometric Series 2nd Edition, en:Cambridge University Press.
Andrews, G. E., Askey, R., & Roy, R. (1999). Special functions. en:Cambridge university press.
Askey, Richard; Wilson, James (1985), "Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials", Memoirs of the en:American Mathematical Society, 54 (319): iv+55, doi:10.1090/memo/0319, ISBN 978-0-8218-2321-7, ISSN 0065-9266, MR 0783216

wolfram.com

reference.wolfram.com

Mathematicaにある特殊関数の一覧