On the several identities of Riemann zeta-function
The author records various identities, as an example: If an integer \(n>4\), then \[ 24\sum_{a+b+c+d=n} \zeta(2a)\zeta(2b)\zeta(2c)\zeta(2d)= (n+1)(2n+1)(2n+3) \zeta(2n)-48n\zeta(2)\zeta(2n-2).\tag{1} \] Also, he points out a correction in the formula \[ \begin{multlined} 96\sum_{a+b+c+d+e=n} \zeta(2a)\zeta(2b)\zeta(2c)\zeta(2d)\zeta(2e)= \\ =(n+1)(n+2)(2n+1)(2n+3) \zeta(2n)-60n(n+1)\zeta(2)\zeta(2n-2)+ 144\zeta^ 2(2) \zeta(2n-4) \end{multlined} \tag{2} \] in which the constant 144 should be 216. The formula (2) was obtained by the reviewer in [Indian J. Pure Appl. Math. 18, 794-800 (1987; Zbl 0625.10031)]. This correction is trivial and it can be seen easily from the equation (3.1.6) of the above paper. In the following paper [Indian J. Pure Appl. Math. 18, 891-895 (1987; Zbl 0635.10036)] much more has been proved by the reviewer jointly with \textit{K. Ramachandra}. The method of the paper under review is not very different from the above mentioned paper.
scientific article; zbMATH DE number 62547