Degenerate Pochhammer symbol, degenerate Sumudu transform, and degenerate hypergeometric function with applications

Abstract

In the paper, we first define a degenerate Pochhammer symbol by using the degenerate gamma function and investigate its properties. By using the degenerate Pochhammer symbol, we introduce and investigate a degenerate hypergeometric function. We also define a degenerate Sumudu transform and investigate its properties by using degenerate exponential function. Finally, we give certain the integral representations, derivative formulas, integral transforms, factional calculus applications, and generating functions of the degenerate hypergeometric function.

Keywords

• degenerate Pochhammer symbol
• degenerate Sumudu transform
• degenerate hypergeometric function
• gamma function
• degenerate gamma function
• beta function
• generalized hypergeometric function
• Laplace transform
• degenerate Laplace transform
• Stieltjes transform
• Laguerre transform
• generating function
• fractional calculus operator

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