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Derivatives of any Horn-type hypergeometric functions with respect to their parameters - MaRDI portal

Derivatives of any Horn-type hypergeometric functions with respect to their parameters (Q2230172)

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scientific article

Language	Label	Description	Also known as
English	Derivatives of any Horn-type hypergeometric functions with respect to their parameters	scientific article

Statements

scholarly article

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Derivatives of any Horn-type hypergeometric functions with respect to their parameters (English)

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Vladimir V. Bytev

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Bernd A. Kniehl

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publication date

17 September 2021

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full work available at URL

https://arxiv.org/abs/1712.07579

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describes a project that uses

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MaRDI profile type

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Summations for certain series containing the digamma function

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A reduction formula for the Kampé de Fériet function

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Closed-form summations of certain hypergeometric-type series containing the digamma function

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Derivatives of any order of the Gaussian hypergeometric function<sub>2</sub><i>F</i><sub>1</sub>(<i>a</i>,<i>b</i>,<i>c</i>;<i>z</i>) with respect to the parameters<i>a</i>,<i>b</i>and<i>c</i>

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Derivatives of any order of the hypergeometric function<sub><i>p</i></sub><i>F<sub>q</sub></i>(<i>a</i><sub>1</sub>, …,<i>a<sub>p</sub></i>;<i>b</i><sub>1</sub>, …,<i>b<sub>q</sub></i>;<i>z</i>) with respect to the parameters<i>a<sub>i</sub></i>and<i>b<sub>i</sub></i>

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Derivatives of Horn hypergeometric functions with respect to their parameters

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Parameter derivatives of the generalized hypergeometric function

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A new approach to the epsilon expansion of generalized hypergeometric functions

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Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions

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Parameter derivatives of the jacoby polynomials and the gaussian hypergeometric function

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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals

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Analytic tools for Feynman integrals

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Differential reduction of generalized hypergeometric functions from Feynman diagrams: one-variable case

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Some exact results for <i>N</i>-point massive Feynman integrals

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A new hypergeometric representation of one-loop scalar integrals in \(d\) dimensions

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Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

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Analytic result for the one-loop scalar pentagon integral with massless propagators

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\(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections

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Massive Feynman diagrams and inverse binomial sums

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On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters

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Symbolic expansion of transcendental functions

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Expansion around half-integer values, binomial sums, and inverse binomial sums

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XSummer -- transcendental functions and symbolic summation in form

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Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters

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Hypexp 2, expanding hypergeometric functions about half-integer parameters

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NumExp: numerical epsilon expansion of hypergeometric functions

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Analytic computing methods for precision calculations in quantum field theory

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HYPERDIRE HYPERgeometric functions DIfferential REduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Horn-type hypergeometric functions of two variables

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Hypergeometric functions differential reduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: \(F_D\) and \(F_S\) Horn-type hypergeometric functions of three variables

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HYPERDIRE -- hypergeometric functions differential reduction: Mathematica-based packages for the differential reduction of generalized hypergeometric functions: Lauricella function \(F_C\) of three variables

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Two-loop sunset diagrams with three massive lines

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Two-loop diagrams in nonrelativistic QCD with elliptics

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Multiple Hypergeometric Series: Appell Series and Beyond

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Nuclear Physics B

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1016/J.NUCLPHYSB.2019.114911

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Sitelinks

Mathematics(1 entry)

mardi Publication:2230172

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