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On Relationships Between Classical Pearson Distributions and Gauss Hypergeometric Function

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Abstract

In this paper, it is shown that the classical Pearson distributions and Gauss hypergeometric function satisfy a unique differential equation of hypergeometric type. Hence, they are directly related to each other. This connection leads to some new integral relations between them. For instance, two special cases of Pearson distributions, namely the generalized T distribution and Beta distribution, are considered and their direct relationships with Gauss hypergeometric function are obtained.

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Authors and Affiliations

  1. Department of Mathematics, K.N.Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

    Mohammad Masjed-Jamei

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  1. Mohammad Masjed-Jamei
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Correspondence to Mohammad Masjed-Jamei.

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Masjed-Jamei, M. On Relationships Between Classical Pearson Distributions and Gauss Hypergeometric Function. Acta Appl Math 109, 401–411 (2010). https://doi.org/10.1007/s10440-008-9324-1

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  • DOI: https://doi.org/10.1007/s10440-008-9324-1

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