Harmonic-binomial Euler-like sums via expansions of (arcsin x)p

In this paper we evaluate Euler-like sums involving harmonic/odd harmonic numbers and central binomial coefficients by using the expansion for powers of the inverse sine function. We also evaluate a number of integrals which in turn give rise to new central binomial coefficient and harmonic number identities.

Automated summary

In this paper, we evaluate a class of Euler-like sums involving harmonic/odd harmonic numbers and central binomial coefficients using the expansion for powers of the inverse sine function. We also evaluate several integrals that lead to new identities for central binomial coefficients and harmonic numbers.