Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions

Zhong-Xuan Mao; Jing-Feng Tian

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arXiv · 2601.18332

Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions

Zhong-Xuan Mao·Jing-Feng Tian

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Abstract

In this paper, we investigate recurrence relations for the Maclaurin coefficients of the products of a elementary function and the Bessel function of the first kind $\mathcal{J}(z) = h(z) J_\nu(z)$ and the modified Bessel function of the first kind $\mathcal{I}(z) = h(z) I_\nu(z)$ in the complex plane corresponding to several specific choices of $h(z)$. In particular, we specialize $h(z)$ as $e^{pz}$, $(1-\theta z)^p$, $e^{-p \arctan z}$, $\sin(pz)$, $\cos(pz)$, $\sinh(pz)$, $\cosh(pz)$, $\arcsin(pz)$ and $\arccos(pz)$.

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BibTeX RIS

Zhong-Xuan Mao, Jing-Feng Tian. 2026-01-26. Recurrence Relations for the Maclaurin Coefficients of Products of Elementary Functions and the Bessel Functions. https://arxiv.org/abs/2601.18332

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