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

Richard B. Paris; Vladimir V. Vinogradov

doi:10.1007/s10986-020-09488-4

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 journal › Article

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 language	English
Number of pages	11
Journal	Lithuanian Mathematical Journal
Early online date	28 Jul 2020
DOIs	https://doi.org/10.1007/s10986-020-09488-4
Publication status	E-pub ahead of print - 28 Jul 2020

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Paris, R. B., & Vinogradov, V. V. (2020). The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton–Watson processes. Lithuanian Mathematical Journal. https://doi.org/10.1007/s10986-020-09488-4

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AB - 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.

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