Abstract

We give closed forms for the series ∑_{m=1}^{∞} \frac{(2x)^{2m+2k}}{m^{2}(m+k)\binom{2m}{m}} and ∑_{m=1}^{∞} \frac{(2x)^{2m}(−1)^{m+k}}{m^{2}(m+k)\binom{2m}{m}} for integers k ≥ 0.