## Taiwanese Journal of Mathematics

### A GENERALIZATION OF BESSEL’S INTEGRAL FOR THE BESSEL COEFFICIENTS

Per W. Karlsson

#### Abstract

We derive an integral over the $m$-dimensional unit hypercube that generalizes Bessel’s integral for $J_n(x)$. The integrand is $G(x\psi(t)) \exp(−2\pi i n \cdot t)$, where $G$ is analytic, and $\psi(t) = e^{2\pi it_1} + \ldots + e^{2\pi it_m} + e^{−2\pi i(t_1+...+t_m)}$, while n is a set of non-negative integers. In particular, we consider the case when $G$ is a hypergeometric function $_{p}F_q$.

#### Article information

Source
Taiwanese J. Math., Volume 11, Number 2 (2007), 289-294.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404691

Digital Object Identifier
doi:10.11650/twjm/1500404691

Mathematical Reviews number (MathSciNet)
MR2333348

Zentralblatt MATH identifier
1122.33002

Subjects
Primary: 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$

#### Citation

Karlsson, Per W. A GENERALIZATION OF BESSEL’S INTEGRAL FOR THE BESSEL COEFFICIENTS. Taiwanese J. Math. 11 (2007), no. 2, 289--294. doi:10.11650/twjm/1500404691. https://projecteuclid.org/euclid.twjm/1500404691