Ramanujan-like series for $$frac{1}{pi }$$ involving harmonic numbers

We introduce new classes of Ramanujan-like series for (frac{1}{pi }), by devising methods for evaluating harmonic sums involving squared central binomial coefficients, such as the Ramanujan-type series

$$begin{aligned} sum _{n=1}^{infty } frac{left( {begin{array}{c}2 n nend{array}}right) ^2 left( H_n^2+H_n^{(2)}right) }{16^n (2 n-1)} = frac{4 pi }{3}-frac{32 ln ^2(2) - 32 ln (2) + 16 }{pi } end{aligned}$$

introduced in this article. While the main technique used in this article is based on the evaluation of a parameter derivative of a beta-type integral, we also show how new integration results involving complete elliptic integrals may be used to evaluate Ramanujan-like series for (frac{1}{pi }) containing harmonic numbers.