• On Ramanujan asymptotic expansions and inequalities for hypergeometric functions

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      https://www.ias.ac.in/article/fulltext/pmsc/108/02/0095-0108

    • Keywords

       

      Hypergeometric functions; gamma function; elliptic integrals

    • Abstract

       

      In this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functionsF(a,b;c;x), c ≤a + b, near the singularityx = 1. Further, we obtain monotonous properties of the quotient of two hypergeometric functions and inequalities for certain combinations of them. Finally, we also solve an open problem of finding conditions ona, b > 0 such that 2F(−a,b;a +b;r2) < (2−r2)F(a,b;a +b;r2) holds for all r∈(0,1).

    • Author Affiliations

       

      R Balasubramanian1 S Ponnusamy1 2

      1. Institute of Mathematical Sciences, C.I.T. Campus, Chennai - 600113, India
      2. Department of Mathematics, Indian Institute of Technology, Institution of Engineers Building, Panbazar, Guwahati - 781 001, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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