Bessel equation and Bessel function on T(q,h)

被引:4
|
作者
Yantir, Ahmet [1 ]
Yantir, Burcu Silindir [2 ]
Tuncer, Zehra [2 ]
机构
[1] Yasar Univ, Fac Sci & Letters, Dept Math, Izmir, Turkey
[2] Dokuz Eylul Univ, Fac Sci, Dept Math, Izmir, Turkey
关键词
Nabla generalized quantum binomial; nabla (q; h)-Taylor series; h)-analytic functions; (q; h)-Bessel equation; h)-Bessel function;
D O I
10.3906/tar-2201-142
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:3300 / 3322
页数:24
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