Related papers: On the all-order epsilon-expansion of generalized …
We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows…
We prove the following theorems: 1) The Laurent expansions in epsilon of the Gauss hypergeometric functions 2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z), 2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z),…
It is proved that the Laurent expansion of the following Gauss hypergeometric functions, 2F1(I1+a*epsilon, I2+b*ep; I3+c*epsilon;z), 2F1(I1+a*epsilon, I2+b*epsilon;I3+1/2+c*epsilon;z), 2F1(I1+1/2+a*epsilon, I2+b*epsilon; I3+c*epsilon;z),…
We briefly sketch a proof concerning the structure of the all-order epsilon-expansions of generalized hypergeometric functions with special sets of parameters.
We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple…
The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the construction of the $\epsilon$-expansion. As an example, we present a detailed discussion of…
Assumed that the parameters of a generalized hypergeometric function depend linearly on a small variable $\varepsilon$, the successive derivatives of the function with respect to that small variable are evaluated at $\varepsilon=0$ to…
In this talk, we discuss the algorithm for the construction of analytical coefficients of higher order epsilon expansion of some Horn type hypergeometric functions of two variables around rational values of parameters.
Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…
We review the hypergeometric function approach to Feynman diagrams. Special consideration is given to the construction of the Laurent expansion. As an illustration, we describe a collection of physically important one-loop vertex diagrams…
Hypergeometric functions provide a useful representation of Feynman diagrams occuring in precision phenomenology. In dimension regularization, the epsilon-expansion of these functions about d=4 is required. We discuss the current status of…
The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or…
We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
Application of the geometrically-inspired representations to the epsilon-expansion of the two-point function with different masses is considered. Explicit result for an arbitrary term of the expansion is obtained in terms of log-sine…
Some problems related to construction of the epsilon-expansion of dimensionally regulated Feynman integrals are discussed. For certain classes of diagrams, an arbitrary term of the epsilon-expansion can be expressed in terms of log-sine…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is…
We review the series solutions of the general and single-confluent Heun equations in terms of powers, ordinary-hypergeometric and confluent-hypergeometric functions. The conditions under which the expansions reduce to finite sums as well as…
Hypergeometric functions of one and many variables play an important role in various branches of modern physics and mathematics. Often we have hypergeometric functions with indices linear dependent on a small parameter with respect to which…