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Evaluation of Appell functions in relativistic Coulomb-Dirac form factors

U Becker, N Grun and W Scheid

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The continuum-continuum transition matrix elements of the scalar and vector potentials of a pure Coulomb field with exact Dirac wavefunctions can be expressed in terms of generalised hypergeometric functions of two variables denoted as Appell functions. The domain of physical interest for the variables exceeds the convergence region of the original double sum. A method for analytical continuation of the Appell functions is given together with a recipe for their fast calculation.


PACS

02.30.Gp Special functions

MSC

33C20 Generalized hypergeometric series, pFq

33C65 Appell, Horn and Lauricella functions

Subjects

Mathematical physics

Dates

Issue 16 (11 November 1987)



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