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arXiv · 0808.2605

Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions

S. A. Yost·M. Yu. Kalmykov·B. F. L. Ward
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Abstract

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 differential reduction algorithms. As an illustration, we consider the construction of the all-order epsilon-expansion of the Appell hypergeometric function about integer values of the parameters and present an explicit evaluations of the first few terms.

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S. A. Yost, M. Yu. Kalmykov, B. F. L. Ward. 2008-10-06. Differential Reduction Algorithms for the All-Order Epsilon Expansion of Hypergeometric Functions. https://arxiv.org/abs/0808.2605

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