A Lambda Analogue of the Gamma Function and its Properties

Abstract

We consider a generalization of the gamma function which we term as lambda analogue of the gamma function or $\lambda$-gamma function and further, we establish some of its accompanying properties. For the particular case when $\lambda=1$, the results established reduce to results involving the classical gamma function. The techniques employed in proving our results are analytical in nature.

Keywords

• gamma function
• lambda analogue
• $\lambda$-gamma function
• $\lambda$-beta function
• bohr-mollerup theorem
• inequality