Abstract:

We give closed forms for the series $\sum_{m=1}^{\infty}\frac{(2x)^{2m+2k}}{m^{2}(m+k) {2m \choose m}}$ and $\sum_{m=1}^{\infty}\frac{(2x)^{2m}(-1)^{m+k}}{m^{2}(m+k) {2m \choose m}}$ for integers $k \geq 0$.