Growth of power series with nonnegative coefficients, and moments of power series distributions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916195825876992 |
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| author | Cantón, Alicia Fernández, José L. Fernández, Pablo Maciá, Víctor J. |
| author_facet | Cantón, Alicia Fernández, José L. Fernández, Pablo Maciá, Víctor J. |
| contents | Any power series with nonnegative coefficients has an associated family of probability distributions supported on the nonnegative integers. There is a close connection between the function theoretic properties of the power series and the moments of the family of distributions. In this paper, we describe that interplay, provide simpler proofs of some known results by emphasizing the probabilistic perspective, and present some new theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14473 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth of power series with nonnegative coefficients, and moments of power series distributions Cantón, Alicia Fernández, José L. Fernández, Pablo Maciá, Víctor J. Probability Complex Variables 30B10, 30D20, 60E05, 30D15 Any power series with nonnegative coefficients has an associated family of probability distributions supported on the nonnegative integers. There is a close connection between the function theoretic properties of the power series and the moments of the family of distributions. In this paper, we describe that interplay, provide simpler proofs of some known results by emphasizing the probabilistic perspective, and present some new theorems. |
| title | Growth of power series with nonnegative coefficients, and moments of power series distributions |
| topic | Probability Complex Variables 30B10, 30D20, 60E05, 30D15 |
| url | https://arxiv.org/abs/2401.14473 |