On derivatives of hypergeometric functions and classical polynomials with respect to parameters

P. C. Sofotasios; Yu A. Brychkov

doi:10.1080/10652469.2018.1504042

On derivatives of hypergeometric functions and classical polynomials with respect to parameters

P. C. Sofotasios, Yu A. Brychkov

Electrical Engineering

Russian Academy of Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.

Original language	British English
Pages (from-to)	852-865
Number of pages	14
Journal	Integral Transforms and Special Functions
Volume	29
Issue number	11
DOIs	https://doi.org/10.1080/10652469.2018.1504042
State	Published - 2 Nov 2018

Keywords

33C20
33C45
Bessel polynomial
C33
Charlier polynomial
continuous Hahn polynomial
differentiation
Gegenbauer polynomial
Hahn polynomial
hypergeometric functions
Jacobi polynomial
Krawtchouk polynomial
Laguerre polynomial
Legendre function
Meixner polynomial
Special functions

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10.1080/10652469.2018.1504042

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@article{97ebe5cc8ed24bc2a838c2b2f36ffe7c,

title = "On derivatives of hypergeometric functions and classical polynomials with respect to parameters",

abstract = "Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.",

keywords = "33C20, 33C45, Bessel polynomial, C33, Charlier polynomial, continuous Hahn polynomial, differentiation, Gegenbauer polynomial, Hahn polynomial, hypergeometric functions, Jacobi polynomial, Krawtchouk polynomial, Laguerre polynomial, Legendre function, Meixner polynomial, Special functions",

author = "Sofotasios, {P. C.} and Brychkov, {Yu A.}",

note = "Funding Information: This work was supported by the Russian Foundation for Basic Research under Project No. 17-07-00217. Publisher Copyright: {\textcopyright} 2018, {\textcopyright} 2018 Informa UK Limited, trading as Taylor & Francis Group.",

year = "2018",

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day = "2",

doi = "10.1080/10652469.2018.1504042",

language = "British English",

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journal = "Integral Transforms and Special Functions",

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T1 - On derivatives of hypergeometric functions and classical polynomials with respect to parameters

AU - Sofotasios, P. C.

AU - Brychkov, Yu A.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research under Project No. 17-07-00217. Publisher Copyright: © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2018/11/2

Y1 - 2018/11/2

N2 - Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.

AB - Closed expressions are obtained for derivatives of symbolic order with respect to parameters for the hypergeometric functions, Laguerre, Gegenbauer, Jacobi and some other polynomial.

KW - 33C20

KW - 33C45

KW - Bessel polynomial

KW - C33

KW - Charlier polynomial

KW - continuous Hahn polynomial

KW - differentiation

KW - Gegenbauer polynomial

KW - Hahn polynomial

KW - hypergeometric functions

KW - Jacobi polynomial

KW - Krawtchouk polynomial

KW - Laguerre polynomial

KW - Legendre function

KW - Meixner polynomial

KW - Special functions

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U2 - 10.1080/10652469.2018.1504042

DO - 10.1080/10652469.2018.1504042

M3 - Article

AN - SCOPUS:85053369865

SN - 1065-2469

VL - 29

SP - 852

EP - 865

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

IS - 11

ER -

On derivatives of hypergeometric functions and classical polynomials with respect to parameters

Abstract

Keywords

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