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Gamma Function and Its Functional Equations

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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 Schlömilch gave an interesting additive analogue of the duplication formula. We prove a generalized version of this formula using the theory of hypergeometric functions.

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Authors and Affiliations

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

    Ritesh Goenka & Gopala Krishna Srinivasan

Authors
  1. Ritesh Goenka
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  2. Gopala Krishna Srinivasan
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Correspondence to Ritesh Goenka or Gopala Krishna Srinivasan.

Additional information

Ritesh Goenka graduated from IIT Bombay with a Bachelor of Technology in Computer Science and Engineering. He will next be joining the master’s program in Mathematics at the University of British Columbia, Canada.

Gopala Krishna Srinivasan is presently a Professor of Mathematics at IIT Bombay. He was conferred the S. P. Sukhatme Excellence in Teaching Award on September 5, 2016.

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Goenka, R., Srinivasan, G.K. Gamma Function and Its Functional Equations. Reson 26, 367–386 (2021). https://doi.org/10.1007/s12045-021-1136-x

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