Some special functions and cylindrical diffusion equation on α -time scale
Year: 2025
Type: article
Abstract: This article is dedicated to present various concepts on α \alpha -time scale, including power series, Taylor series, binomial series, exponential function, gamma function, and Bessel functions of the first kind. We introduce the α \alpha -exponential function as a series, examine its absolute and uniform convergence, and establish its additive identity by employing the α \alpha -Gauss binomial formula. Furthermore, we define the α \alpha -gamma function and prove α \alpha -analogue of the Bohr-Mollerup theorem. Specifically, we demonstrate that the α \alpha -gamma function is the unique logarithmically convex solution of f ( s + 1 ) = ϕ ( s ) f ( s ) f\left(s+1)=\phi \left(s)f\left(s) , f ( 1 ) = 1 f\left(1)=1 , where ϕ ( s ) \phi \left(s) refers to the α \alpha -number. In addition, we present Euler’s infinite product form and asymptotic behavior of α \alpha -gamma function. As an application, we propose α \alpha -analogue of the cylindrical diffusion equation, from which α \alpha -Bessel and modified
Source: Demonstratio Mathematica
Institutions: Dokuz Eylül University, Yaşar University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4411163435