Let denote the trilogarithm function. Prove that

where denotes the Riemann zeta function.

*(Seraphim Tsipelis)*

**Solution **[by Ramya Datta]

Let us recall the Fourier expansion

Hence

A site of university mathematics

Home » Uncategorized » Sum with trilogarithm

Let denote the trilogarithm function. Prove that

where denotes the Riemann zeta function.

*(Seraphim Tsipelis)*

**Solution **[by Ramya Datta]

Let us recall the Fourier expansion

Hence