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arXiv · 0906.1861

On singular univariate specializations of bivariate hypergeometric functions

Raimundas Vidunas
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Abstract

It is tempting to evaluate F2(x,1) and similar univariate specializations of Appell's functions by evaluating the apparent power series at x=0 straight away using the Gauss formula for 2F1(1). But this kind of naive evaluation can lead to errors as the 2F1(1) coefficients might eventually diverge; then the actual power series at x=0 might involve branching terms. This paper demonstrates these complications on concrete examples.

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Raimundas Vidunas. 2009-06-10. On singular univariate specializations of bivariate hypergeometric functions. https://doi.org/10.1016/j.jmaa.2009.10.018

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