Multiple hypergeometric series -- Appell series and beyond

Abstract

This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provides a small collection of basic material on multiple hypergeometric series of Appell-type and of more general series of related type.

17 pages

References in corpus (4)

• HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: Horn hypergeometric functions of two variables
• HYPERDIRE: HYPERgeometric functions DIfferential REduction: MATHEMATICA based packages for differential reduction of generalized hypergeometric functions pFq, F1,F2,F3,F4
• A massive Feynman integral and some reduction relations for Appell functions
• Monodromy of A-hypergeometric functions

Cited by in corpus (14)

• Traversable Wormholes via a Double Trace Deformation
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Bulk View of Teleportation and Traversable Wormholes
• The Unpolarized and Polarized Single-Mass Three-Loop Heavy Flavor Operator Matrix Elements $A_{gg,Q}$ and $\Delta A_{gg,Q}$
• The SAGEX Review on Scattering Amplitudes, Chapter 4: Multi-loop Feynman Integrals
• On Conformal Block, Crossing Kernel and Multi-variable Hypergeometric Functions
• Transparentizing Black Holes to Eternal Traversable Wormholes
• Analytic continuations and numerical evaluation of the Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$ and their Application to Feynman Integrals
• Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
• q-derivatives of multivariable q-hypergeometric function with respect to their parameters
• Radiation of inertial scalar particles in the de Sitter universe
• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change
• Some new formulas for Appell series over finite fields
• On the sojourn time of a batch in the $M^{[X]}/M/1$ Processor Sharing Queue