All-Order ε-Expansion of Gauss Hypergeometric Functions with Integer and Half-Integer Values of Parameters
نویسنده
چکیده
It is proved that the Laurent expansion of the following Gauss hypergeometric functions, are an arbitrary integer nonnegative numbers, a, b, c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients of Laurent expansion is constructed. Some particular cases of Gauss hypergeometric functions are also discussed.
منابع مشابه
All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
It is proved that the Laurent expansion of the following Gauss hypergeometric functions, are an arbitrary integer nonnegative numbers, a, b, c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients o...
متن کاملGauss hypergeometric function : reduction , ε - expansion for integer / half - integer parameters and Feynman diagrams
The Gauss hypergeometric functions 2 F 1 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 half-integer values of parameters there are only three types of algebraically independent Gauss hyperge-ometric functions. The ε-expansion of functions of one of ...
متن کاملMultiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter
We continue the study of the construction of analytical coefficients of the εexpansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple (inverse) binomial sums
متن کاملOn the all-order epsilon-expansion of generalized hypergeometric functions with integer values of parameters
We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iterated solutions to the differential equations associated with hypergeometric functions to prove the following result: Theorem 1: The epsilon-expansion of a generalized hypergeome...
متن کامل/ 04 06 26 9 v 1 3 0 Ju n 20 04 Series and ε - expansion of the hypergeometric functions
Recent progress in analytical calculation of the multiple {inverse, binomial, harmonic} sums , related with ε-expansion of the hypergeometric function of one variable are discussed. 1. In the framework of the dimensional regular-ization [1] many Feynman diagrams can be written as hypergeometric series of several variables [2] (some of them can be equal to the rational numbers). This result can ...
متن کامل