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arXiv · 2412.10938

On integral representations of $q$-difference operators and their applications

Antonio Cáceres·Alberto Lastra·Sławomir Michalik·Maria Suwińska
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Abstract

Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through the so-called $(p,q)$-differential operator, for which a kernel-like function is provided, generating the sequence of $(p,q)$-factorials.

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Antonio Cáceres, Alberto Lastra, Sławomir Michalik, Maria Suwińska. 2024-12-14. On integral representations of $q$-difference operators and their applications. https://doi.org/10.1007/s00208-026-03323-w

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