English

On singular univariate specializations of bivariate hypergeometric functions

Complex Variables 2013-10-04 v2 Classical Analysis and ODEs

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.

Keywords

Cite

@article{arxiv.0906.1861,
  title  = {On singular univariate specializations of bivariate hypergeometric functions},
  author = {Raimundas Vidunas},
  journal= {arXiv preprint arXiv:0906.1861},
  year   = {2013}
}

Comments

10 pages

R2 v1 2026-06-21T13:11:44.298Z