A new representation of the extended k-gamma function with applications

In this study, a new series representation of the extended k-gamma function is investigated. A new representation expresses this function as an infinite sum of delta functions. Several researchers have examined this family of functions, but no study has been conducted dealing with the fractional kinetic equation. A new representation proves useful to solve the fractional kinetic equation involving an extended k-gamma function. Particular cases involving the original gamma function are discussed as corollaries. Such an application of the gamma function is not possible by using known representations; nevertheless, using this representation, new fractional transform formulae are evaluated. A new representation is also worthwhile to compute new integrals of products of the extended k-gamma functions, proving to be reliable with known identities. Several distributional properties of the extended k-gamma function are also discussed using Fourier transform.

Automated summary

This study investigates a new series representation of the extended k-gamma function, which proves useful for solving fractional kinetic equations. The new representation also helps compute new integrals and discuss distributional properties of the extended k-gamma function via Fourier transform.