PreprintarXiv licencearXiv
On one-sided series of Bessel functions of the first kind: ∑m=0∞ (± 1)m JNm+p(x)
Abstract
We present generic expressions for one-sided series of Bessel functions of the first kind: ∑m=0∞ JNm+p(x) and ∑m=0∞ (−1)m JNm+p(x). The result is expressed in terms of incomplete Lipschitz-Hankel integrals of Bessel functions of the first kind, which can be represented as Kampé de Fériet functions.
Related
- Sharp two-sided bounds for the product of modified Bessel functions and for its logarithmic derivative
- Meromorphic Solutions of Certain Kind of Non-Linear Differential equation with finite sums of Exponential Functions
- Two refined Wilf-equivalences for patterns of length 4 and a conjecture on Dumont permutations of the first kind
- The Marvelous Meixner Polynomials: Second Kind, First Class
- Big Bounce, Big Crunch Cycle: Full Vector--Gravity Coupling, Fixed-Point Instability, and Stable Limit Cycle in a Five-Dimensional Bessel--Klein--Gordon Framework Paper I of a two-part series
BibTeX
@misc{kornilov2026onesided,
title = {{On one-sided series of Bessel functions of the first kind: $\sum_m=0^\infty (\pm 1)^m J_Nm+p(x)$}},
author = {Matwey V. Kornilov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09216},
eprint = {2609.09216},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09216},
}
RIS
TY - UNPB
TI - On one-sided series of Bessel functions of the first kind: ∑_m=0^∞ (± 1)^m J_Nm+p(x)
AU - Matwey V. Kornilov
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.09216
UR - https://arxiv.org/abs/2609.09216
AB - We present generic expressions for one-sided series of Bessel functions of the first kind: ∑_m=0^∞ J_Nm+p(x) and ∑_m=0^∞ (−1)^m J_Nm+p(x). The result is expressed in terms of incomplete Lipschitz-Hankel integrals of Bessel functions of the first kind, which can be represented as Kampé de Fériet functions.
ER -