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 |
Keywords
- Asymptotic behaviour
- Characteristic function
- Discrete distribution with power tail
- Fourier transform
- Galton-Watson process
- Hypergeometric function with large parameters
- Law of the total progeny
- Probability-generating function
- Scaled Sibuya distribution