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      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/026/03/0367-0386

    • Keywords

       

      Gamma function, Euler’s reflection formula, Legendre’s duplication formula.

    • Abstract

       

      In this article, we look at some of the less explored aspects of the gamma function. We provide a new proof of Euler’s reflection formula and discuss its significance in the theory of special functions. We also discuss the solution of Landau to a problem posed by Legendre, concerning the determination of values of the gamma function using functional identities. In 1848, Oscar Schlomilch gave an interesting additive analogue of the duplication formula. We prove a generalized version of this formula using the theory of hypergeometric functions.

    • Author Affiliations

       

      Ritesh Goenka1 Gopala Krishna Srinivasan1

      1. Indian Institute of Technology Bombay, Powai Mumbai, Maharashtra 400076
    • Dates

       
  • Resonance – Journal of Science Education | News

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