On singular univariate specializations of bivariate hypergeometric functions |
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Authors: | Raimundas Vidūnas |
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Affiliation: | Kobe University, Department of Mathematics, Rokko-dai 1-1, Kobe 657-8501, Japan |
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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 by concrete examples. |
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Keywords: | Appell functions Double hypergeometric series Analytic continuation |
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