All order ε-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
نویسندگان
چکیده
منابع مشابه
All-Order ε-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...
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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...
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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...
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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 ...
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We prove the following theorems: 1) The Laurent expansions in ε of the Gauss hypergeometric functions 2F1(I1 + aε, I2 + bε; I3 + p q + cε; z), 2F1(I1 + p q + aε, I2 + p q + bε; I3+ p q + cε; z) and 2F1(I1+ p q +aε, I2+ bε; I3 + p q + cε; z), where I1, I2, I3, p, q are arbitrary integers, a, b, c are arbitrary numbers and ε is an infinitesimal parameter, are expressible in terms of multiple poly...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2007
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2007/02/040