On singular univariate specializations of bivariate hypergeometric functions. (English) Zbl 1226.33006
Summary: It is tempting to evaluate \(F_2(x,1)\) and similar univariate specializations of Appell’s functions by evaluating the apparent power series at \(x=0\) straight away using the Gauss formula for \(_2F_1(1)\). But this kind of naive evaluation can lead to errors as the \(_2F_1(1)\) coefficients might eventually diverge; then the actual power series at \(x=0\) might involve branching terms. This paper demonstrates these complications by concrete examples.
MSC:
| 33C65 | Appell, Horn and Lauricella functions |
| 33C20 | Generalized hypergeometric series, \({}_pF_q\) |
References:
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