The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton–Watson processes

Richard B. Paris*, Vladimir V. Vinogradov

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    We evaluate a weighted sum of Gauss hypergeometric functions for certain ranges of the argument, weights and parameters. We establish the domain of absolute convergence of this series by determining the growth of the hypergeometric function for large summation index. We present an application to Galton–Watson branching processes arising in the theory of stochastic processes. We introduce a new class of positive integer-valued distributions with power tails.
    Original languageEnglish
    Number of pages11
    JournalLithuanian Mathematical Journal
    Early online date28 Jul 2020
    DOIs
    Publication statusE-pub ahead of print - 28 Jul 2020

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