New analytic continuations for the Appell $F_4$ series from quadratic transformations of the Gauss $_{2}F_1$ function - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

New analytic continuations for the Appell $F_4$ series from quadratic transformations of the Gauss $_{2}F_1$ function

Résumé

We present new analytic continuation formulas for the Appell $F_4(a,b;c,d;x,y)$ double hypergeometric series where $d=a-b+1$, which allows quadratic transformations of the Gauss ${}_2F_1$ hypergeometric function to be used in the intermediate steps of the derivation. Such formulas are of relevance to loop calculations of quantum field theory where they can been used, for instance, to obtain new series representations of the two-loop massive sunset Feynman diagram. The analytic continuation procedure introduced in this paper is also sufficiently general so as to find uses elsewhere.

Dates et versions

hal-02863194 , version 1 (10-06-2020)

Identifiants

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B. Ananthanarayan, Samuel Friot, Shayan Ghosh, Anthony Hurier. New analytic continuations for the Appell $F_4$ series from quadratic transformations of the Gauss $_{2}F_1$ function. 2020. ⟨hal-02863194⟩
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