Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3334
Abstract
This article is devoted to present nabla $(q, h)$-analogues of Bessel equation and Bessel function. In order to construct series solution of nabla $(q, h)$-Bessel equation, we present nabla $(q, h)$-analysis regarding nabla generalized quantum binomial, nabla $(q,h)$-analogues of Taylor's formula, Gauss's binomial formula, Taylor series, analytic functions, analytic exponential function with its fundamental properties, analytic trigonometric and hyperbolic functions. We emphasize that nabla $(q, h)$-Bessel equation recovers classical, $h$- and $q$-discrete Bessel equations. In addition, we establish nabla $(q, h)$-Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate its reductions. Finally, we develop modified nabla $(q,h)$-Bessel equation, modified nabla $(q,h)$-Bessel function and its relation with nabla $(q,h)$-Bessel function.
Keywords
Nabla generalized quantum binomial, nabla $(q, h)$-Taylor series, nabla $(q, h)$-analytic functions, nabla $(q, h)$-Bessel equation, nabla $(q, h)$-Bessel function
First Page
3300
Last Page
3322
Recommended Citation
YANTIR, AHMET; YANTIR, BURCU SİLİNDİR; and TUNCER, ZEHRA
(2022)
"Bessel equation and Bessel function on $\mathbb{T}_{(q,h)}$,"
Turkish Journal of Mathematics: Vol. 46:
No.
8, Article 16.
https://doi.org/10.55730/1300-0098.3334
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss8/16
