On the Carlitz-Mehler formula for Hermite polynomials

Manish Chaurasia

doi:10.48550/arxiv.2508.12676

August 18, 2025Open Access

On the Carlitz-Mehler formula for Hermite polynomials

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Key Points

A direct proof of a further generalization of the Carlitz-Mehler formula is presented, enhancing understanding of Hermite polynomials.
This work builds upon previous proofs by Srivastava et al. while establishing clearer connections among extensions and formulations.
The method employed offers a more transparent approach to understanding the Carlitz-Mehler transformations in Hermite polynomial contexts.
This generalization may facilitate further research in related mathematical fields and applications, emphasizing its importance.

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Implication

Direct proof of further generalization of Carlitz's formula for Hermite polynomials, indicating its significance and extensions.

Abstract

Carlitz proved a few generalizations of Mehler's formula. Later, Srivastava et al. gave a new proof for some extensions of Carlitz's formula. Here, a direct proof of the further generalization is given.

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Manish Chaurasia (2025) studied this question.

synapsesocial.com/papers/68d913a34ddcf71ba560ba4c https://doi.org/10.48550/arxiv.2508.12676

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On the Carlitz-Mehler formula for Hermite polynomials

Key Points

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Implication

Abstract

Discussion

Cite This Study

On the Carlitz-Mehler formula for Hermite polynomials

Key Points

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Implication

Abstract

Discussion

Cite This Study

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