On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters

doi:10.1088/1126-6708/2007/11/009

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Mikhail Y. Kalmykov et al JHEP11(2007)009 doi:10.1088/1126-6708/2007/11/009

On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters

Mikhail Y. Kalmykov¹, Bennie F.L. Ward² and Scott A. Yost³

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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 hypergeometric function with integer values of parameters, _pF_p−1(I₁+a₁ε,...,I_p+a_pε;I_p+1+b₁ε,...,I_2p−1+b_p−1;z) , is expressible in terms of generalized polylogarithms with coefficients that are ratios of polynomials. The method used in this proof provides an efficient algorithm for calculating of the higher-order coefficients of Laurent expansion.

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Journal of High Energy Physics

On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters

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