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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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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DOI: https://doi.org/10.1007/s12045-021-1136-x