New definite integrals and a two-term dilogarithm identity

F. M. S. Lima

Among the several proofs known for ${\sum }_{n=1}^{\infty }1/n^2={\pi }^2/6$, the one by Beukers, Calabi, and Kolk involves the evaluation of $\,\int_0^1 {\int_0^1{1/(1-x^2 y^2) \, dx}…