English

On a fundamental system of solutions of a certain hypergeometric equation

Classical Analysis and ODEs 2014-08-05 v2

Abstract

We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gau\ss's 2F1{}_2 F_{1}, Thomae's LFL1{}_L F_{L-1} and Appell-Lauricella's FDF_D. In particular, we present a fundamental system of solutions with a characteristic local behavior by means of Euler-type integral representations. We also discuss how they are related to the theory of isomonodromic deformations or Painlev\'e equations.

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Cite

@article{arxiv.1407.8052,
  title  = {On a fundamental system of solutions of a certain hypergeometric equation},
  author = {Teruhisa Tsuda},
  journal= {arXiv preprint arXiv:1407.8052},
  year   = {2014}
}

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19 pages