A massive Feynman integral and some reduction relations for Appell functions

DOI10.1063/1.2821256zbMath1153.81433arXiv0711.2742OpenAlexW3103744982MaRDI QIDQ3544563

M. A. Shpot

Publication date: 8 December 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2742

Mathematics Subject Classification ID

Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Appell, Horn and Lauricella functions (33C65)

Related Items (14)

The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ NumExp: numerical epsilon expansion of hypergeometric functions ⋮ Representation of the Coulomb matrix elements by means of Appell hypergeometric function \(F_2\) ⋮ \texttt{AlgRel.wl}: algebraic relations for the product of propagators in Feynman integrals ⋮ On conjectured local generalizations of anisotropic scale invariance and their implications ⋮ Reduction formulas for the Appell and Humbert functions ⋮ On integral representations and asymptotics of some hypergeometric functions in two variables ⋮ Finding new relationships between hypergeometric functions by evaluating Feynman integrals ⋮ A \((p, \nu)\)-extension of the Appell function \(F_1(\cdot)\) and its properties ⋮ Some results on the first Appell matrix functionF₁(A,B,B′,C;z,w) ⋮ The Feynman integral in ℝ¹⊕ ℝ^mand complex expansion of₂F₁ ⋮ Two-loop Feynman integrals for ϕ4 theory with long-range correlated disorder ⋮ Method of continual addition theorems and integral relations between the Coulomb functions and the Appell function \(F_1\) ⋮ Some summation theorems for Clausen's hypergeometric functions with unit argument

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new hypergeometric representation of one-loop scalar integrals in \(d\) dimensions
• Some reduction and transformation formulas for the Appell hypergeometric function \(F_{2}\)
• Feynman diagrams to three loops in three-dimensional field theory
• The H function associated with a certain class of Feynman integrals
• Some integrals involving three modified Bessel functions. I
• New properties of hypergeometric series derivable from Feynman integrals. I. Transformation and reduction formulae
• New properties of hypergeometric series derivable from Feynman integrals II. A generalisation of the H function
• One-loopn-point equivalence among negative-dimensional, Mellin–Barnes and Feynman parametrization approaches to Feynman integrals
• General massive one-loop off-shell three-point functions
• A geometrical angle on Feynman integrals
• W. Gordon’s integral (1929) and its representations by means of Appell’s functions F2, F1, and F3
• On the system of partial differential equations associated with Appell's function F₄
• Some definite integrals associated with the Riemann zeta function
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points

This page was built for publication: A massive Feynman integral and some reduction relations for Appell functions