# Hypergeometric Functions and Feynman Diagrams

@article{Kalmykov2021HypergeometricFA, title={Hypergeometric Functions and Feynman Diagrams}, author={Mikhail Yu. Kalmykov and Vladimir V. Bytev and Bernd A. Kniehl and S. Moch and Bennie F. L. Ward and Scott A. Yost}, journal={Texts \& Monographs in Symbolic Computation}, year={2021} }

The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the constructionof the Y-expansion. As an example, we present a detailed discussion of the construction of the Y-expansion of the Appell function 3 around rational values of parameters via an iterative solution of differential equations. Another interesting example is the Puiseux-type solution involving a differential operator generated by a hypergeometric…

## 10 Citations

Olsson.wl : a Mathematica package for the computation of linear transformations of multivariable hypergeometric functions

- Mathematics
- 2021

The Olsson.wl Mathematica package, which aims to find linear transformations for some classes of multivariable hypergeometric functions, is presented and a companion package, called ROC2.wl, dedicated to the derivation of the regions of convergence of doublehypergeometric series is provided.

Multiple Series Representations of N-fold Mellin-Barnes Integrals.

- MathematicsPhysical review letters
- 2021

The first evaluation of the hexagon and double box conformal Feynman integrals with unit propagator powers is presented, and the method allows the determination of a single "master series" for each series representation, which considerably simplifies convergence studies and/or numerical checks.

Analytic continuation of Lauricella's function F D (N) for large in modulo variables near hyperplanes {z j = z l }

- MathematicsIntegral Transforms and Special Functions
- 2021

We consider the Lauricella hypergeometric function , depending on variables , and obtain formulas for its analytic continuation into the vicinity of a singular set which is an intersection of the…

Analytic continuation of Lauricella's function F D (N) for variables close to unit near hyperplanes {z j = z l }

- MathematicsIntegral Transforms and Special Functions
- 2021

For the Lauricella hypergeometric function with an arbitrary number of variables , we construct formulas for analytic continuation into the vicinity of hyperplanes and their intersections providing…

Analytic Periods via Twisted Symmetric Squares

- Mathematics
- 2021

We study the symmetric square of Picard-Fuchs operators of genus one curves and the thereby induced generalized Clausen identities. This allows the computation of analytic expressions for the periods…

14 72 1 v 2 [ he pth ] 2 5 O ct 2 02 1 Cohomology of Differential Forms and Feynman diagrams October 26 , 2021

- 2021

Co-Homology of Differential Forms and Feynman Diagrams

- MathematicsUniverse
- 2021

In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in light of recent developments. Feynman integrals enter in several…

Cohen-Macaulay Property of Feynman Integrals

- Mathematics
- 2021

: The connection between Feynman integrals and GKZ A -hypergeometric systems has been a topic of recent interest with advances in mathematical techniques and computational tools opening new…

Hypergeometric Structures in Feynman Integrals

- MathematicsArXiv
- 2021

An automated method is devised which recognizes the respective (partial) differential equations related to the corresponding higher transcendental functions and solves these equations through associated recursions of the expansion coefficient of the multivalued formal Taylor series.

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