Growth of power series with nonnegative coefficients, and moments of power series distributions

• Autores: Alicia Cantón Pire, José Luis Fernández Pérez , Pablo Fernández Gallardo, Victor Joel Maciá Medina
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 70, Nº 1, 2026, págs. 161-201
• Idioma: inglés
• DOI: 10.5565/publmat7012607
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• Resumen

  • 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