-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
arXiv:2208.01000 · doi:10.1016/j.nuclphysb.2023.116145
Abstract
We present a new methodology, suitable for implementation on computer, to perform the -expansion of hypergeometric functions with linear dependent Pochhammer parameters in any number of variables. Our approach allows one to perform Taylor as well as Laurent series expansion of multivariable hypergeometric functions. Each of the coefficients of in the series expansion is expressed as a linear combination of multivariable hypergeometric functions with the same domain of convergence as that of the original hypergeometric function. We present illustrative examples of hypergeometric functions in one, two and three variables which are typical of Feynman integral calculus.
Nucl. Phys. B version
References in corpus (13)
- HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
- A Fast Approach to Creative Telescoping
- FIESTA5: numerical high-performance Feynman integral evaluation
- Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
- FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ hypergeometric systems
- A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques
- GKZ-hypergeometric systems for Feynman integrals
- On the all-order epsilon-expansion of generalized hypergeometric functions with integer values of parameters
- Geometrical methods in loop calculations and the three-point function
- Evaluating Feynman integrals by the hypergeometry
- Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d
- Functional reduction of one-loop Feynman integrals with arbitrary masses
- q-derivatives of multivariable q-hypergeometric function with respect to their parameters