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Non-planar elliptic vertex
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abstract
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct integration of parametric representations in terms of iterated integrals. Taking non-planar elliptic vertex as an example we show that in addition to two mentioned methods one can use analytical solution of differential equations in terms of power series. Moreover, in the last case it is possible to obtain the exact in $\epsilon$ results expressible either in terms of generalized hypergeometric or Kamp\'e de F\'eriet functions
Forward citations
Cited by 2 Pith papers
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High-precision numerical evaluation of Lauricella functions
A Mathematica package computes high-precision epsilon-expansions of Lauricella functions using one-dimensional Frobenius series and interpolation.
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$\texttt{PrecisionLauricella}$: package for numerical computation of Lauricella functions depending on a parameter
PrecisionLauricella is a Mathematica package that computes epsilon-expansions of Lauricella F_A, F_B, and F_D functions for n up to 3 using Frobenius-series analytic continuation.
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