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arXiv · 2608.19270

Product formulas for multivariate and matrix-variate confluent hypergeometric functions

Min-Jie Luo·Shu-Ying Shen
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Abstract

In this note, we revisit one of Erdélyi's product formulas for the univariate confluent hypergeometric function ${}_{1}F_{1}$ and extend it to the multivariate confluent hypergeometric functions $Φ_2^{(k)}$, $Ψ_2^{(k)}$, as well as to a certain matrix-variate confluent hypergeometric function. A useful connection related to fractional calculus is also given.

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Min-Jie Luo, Shu-Ying Shen. 2026-08-18. Product formulas for multivariate and matrix-variate confluent hypergeometric functions. https://arxiv.org/abs/2608.19270

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