On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c

Abstract EN

For k∈ℤ, the generalized Arakawa–Kaneko zeta functions with a, b, c parameters are given by the Laplace-Mellin integral ξks,x;a,b,c=1/Γs∫0∞Lik1−ab−t/bt−a−tc−xtts−1dt, where ℜs>0 and x>0 if k≥1, and ℜs>0 and x>k+1 if k≤0.

In this paper, an interpolation formula between these generalized zeta functions and the poly-Bernoulli polynomials with a,b,c parameters is obtained.

Moreover, explicit, difference, and Raabe’s formulas for ξks,x;a,b,c are derived.