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Limits of Jensen polynomials for partitions and other sequences

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Abstract

It was discovered recently by Griffin, Ono, Rolen and Zagier that the Jensen polynomials associated to many sequences have Hermite polynomial limits. We develop this theory in detail, based on the log-polynomial property which is a refinement of log-concavity and log-convexity. Applications to various partition sequences are given. An application to the sequence of factorials leads naturally to evaluating limits of generalized Laguerre polynomials.

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Authors and Affiliations

  1. Department of Math, The CUNY Graduate Center, 365 Fifth Avenue, New York, NY, 10016-4309, USA

    Cormac O’Sullivan

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  1. Cormac O’Sullivan
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Correspondence to Cormac O’Sullivan.

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Communicated by Ilse Fischer.

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Support for this project was provided by a PSC-CUNY Award, jointly funded by The Professional Staff Congress and The City University of New York.

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O’Sullivan, C. Limits of Jensen polynomials for partitions and other sequences. Monatsh Math 199, 203–230 (2022). https://doi.org/10.1007/s00605-022-01714-0

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  • DOI: https://doi.org/10.1007/s00605-022-01714-0

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