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

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

B. Ananthanarayan
(
- Bangalore, Indian Inst. Sci.
)
,
Samuel Friot
(
- IJCLab, Orsay and
- IP2I, Lyon
)
,
Shayan Ghosh
(
- Bonn U., HISKP
)
,
Anthony Hurier
(
- Bangalore, Indian Inst. Sci. and
- IJCLab, Orsay and
- Paris U., IV
)

May 14, 2020

15 pages

e-Print:

2005.07170 [hep-th]

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Abstract: (arXiv)

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.

Note:

15 pages, 7 figures

field theory
Feynman graph
loop integral
Mellin transformation
analytic properties
mathematical methods

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Figures(7)

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