J. Integer Seq. 10(2), Article 07.2.1, 4 p., electronic only (2007)
Summary
Summary: 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 $k \geq 0$.
