Raabe's Formula For Gamma Function Via Riemann-Liouville Fractional Integrals And Generalized Glaisher Constants

Abstract

In this paper, we prove Raabe-type integral formulas for gamma function via left and right sided Riemann-Liouville fractional integrals. As corollaries, we give the left and right sided repeated integration formulas for the log-gamma and related functions. The relationship between the generalized Glaisher constants and aforementioned integrals are investigated.

9 pages