PreprintCC BY 4.0arXiv
Integral representations of high-order derivatives of Bessel functions with respect to the order
Abstract
We derive integral representations for the n-th derivative with respect to the order of Bessel functions of the first, second and third kinds, as well as the modified Bessel function and the Macdonald function. Based on these integral representations, we have developed a highly-efficient algorithm for the numerical evaluation of these derivatives with respect to the order, applicable to any complex argument and any real order.
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BibTeX
@misc{santander2026integral,
title = {{Integral representations of high-order derivatives of Bessel functions with respect to the order}},
author = {J. L. González Santander and David A. Harrington and Angelo Melino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31368},
eprint = {2610.31368},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31368},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Integral representations of high-order derivatives of Bessel functions with respect to the order
AU - J. L. González Santander
AU - David A. Harrington
AU - Angelo Melino
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31368
UR - https://arxiv.org/abs/2610.31368
AB - We derive integral representations for the n-th derivative with respect to the order of Bessel functions of the first, second and third kinds, as well as the modified Bessel function and the Macdonald function. Based on these integral representations, we have developed a highly-efficient algorithm for the numerical evaluation of these derivatives with respect to the order, applicable to any complex argument and any real order.
ER -