Differentiation formulas of some hypergeometric functions with respect to all parameters

DOI10.1016/j.amc.2015.02.017zbMath1338.33018OpenAlexW2022955696MaRDI QIDQ300181

Hongchao Kang, Congpei An

Publication date: 23 June 2016

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.02.017

zbMATH Keywords

applicationshypergeometric functionhypergeometric differential equationdifferential equation method

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items

Quadrature rules and asymptotic expansions for two classes of oscillatory Bessel integrals with singularities of algebraic or logarithmic type, On the integral operators pertaining to a family of incomplete \(I\)-functions, On the approximation of highly oscillatory Volterra integral equations of the first kind via Laplace transform, Approximation for the distribution function of non-central complex Wilks statistic, Monotonicity properties of generalized elliptic integrals with respect to the parameter, \(\epsilon\)-expansion of multivariable hypergeometric functions appearing in Feynman integral calculus, Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis, Efficient quadrature rules for the singularly oscillatory Bessel transforms and their error analysis, Numerical integration of oscillatory Airy integrals with singularities on an infinite interval, Efficient calculation and asymptotic expansions of many different oscillatory infinite integrals, On a family of the incomplete \(H\)-functions and associated integral transforms, A note on pathway fractional integral formulas associated with the incomplete \(H\)-functions

Uses Software

• DLMF
• Cephes

Cites Work

• Numerical evaluation of a class of highly oscillatory integrals involving Airy functions
• Efficient integration for a class of highly oscillatory integrals
• Computation of integrals with oscillatory and singular integrands using Chebyshev expansions
• Computation of integrals with oscillatory singular factors of algebraic and logarithmic type
• The special functions and their approximations. Vol. I, II
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• Parameter derivatives of the jacoby polynomials and the gaussian hypergeometric function
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