On singular univariate specializations of bivariate hypergeometric functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:365

Article

Vidunas, Raimundas

关键词: Appell functions;    Double hypergeometric series;    Analytic continuation;   

DOI  :  10.1016/j.jmaa.2009.10.018

来源: Elsevier

【 摘 要 】

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 F-2(1)(1). But this kind of naive evaluation can lead to errors as the F-2(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. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free