engleski

Asymptotic expansions of integral mean of polygamma functions

We determine the coefficients a_j(s, t) in the asymptotic expansion of integral (or differential) mean of polygamma functions. We derive the recursive relations for polynomials a_j(s, t) and we also derive the main properties of these polynomials as a consequence of the asymptotic formula for shifted variables.

gamma function; psi function; polygamma functions; Bernoulli numbers and polynomials; asymptotic expansion

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