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A Probabilistic Visit to Gauss’s Product Formula for Gamma Function

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Abstract

Some probabilistic methods are used to find a number of combinatorial identities in very elementary manners. One of the identities is for the Laplace transform of a suitable sequence of ordered random variables from an exponential distribution. This identity leads to Gauss’s product formula for gamma function, which itself provides many interesting formulas. Some asymptotics of the underlying distribution are described in connection with some of these identities and Gauss’s product formula.

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References

  • Arnold BC, Balakrishnan N, Nagaraja HN (1992) A First Course in Order Statistics. Wiley, New York

    MATH  Google Scholar 

  • Courant R (1968) Differential and Integral Calculus, vol II. Wiley, New York

  • Cramer H (1946) Mathematical Methods of Statistics. Princeton University Press, Princeton

    MATH  Google Scholar 

  • Feller W (1966) An Introduction to Probability Theory and Its Applications, vol II. Wiley, New York

  • Mukherjea A, Rao M, Suen S (2006) A note on moment generating functions. Stat Probab Lett 76:1185–1189

    Article  MathSciNet  MATH  Google Scholar 

  • Peterson J (2013) A probabilistic proof of a binomial identity. Am Math Mon 120(6):558–562

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Emeritus, Cleveland State University, Cleveland, OH, 44115, USA

    Rasul A. Khan

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  1. Rasul A. Khan
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Correspondence to Rasul A. Khan.

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Khan, R.A. A Probabilistic Visit to Gauss’s Product Formula for Gamma Function. J Indian Soc Probab Stat 19, 97–103 (2018). https://doi.org/10.1007/s41096-018-0036-1

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  • DOI: https://doi.org/10.1007/s41096-018-0036-1

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