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 |
|---|---|
| Pages (from-to) | 385-395 |
| Number of pages | 11 |
| Journal | Lithuanian Mathematical Journal |
| Volume | 60 |
| Issue number | 3 |
| Early online date | 28 Jul 2020 |
| DOIs | |
| Publication status | Published - 31 Jul 2020 |
Fingerprint Dive into the research topics of 'The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton–Watson processes'. Together they form a unique fingerprint.
Cite this
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, 60(3), 385-395. https://doi.org/10.1007/s10986-020-09488-4