The Euler-Riemann zeta function with even arguments in terms of binomial coefficients
In this paper under review, the author proves that the power sum symmetric functions can be expressed in terms of elementary symmetric functions and obtain an equivalent form of a classical identity (see Theorem 1). Furthermore, he expresses the Euler-Riemann zeta functions \(\zeta(2n)\), \(\zeta(4n)\), \(\zeta(6n)\), \(\zeta(8n)\), \(\zeta(10n)\) and \(\zeta(12n)\) in terms of binomial coefficients as sums over all integer partitions of the positive integer \(n\) (see Corollaries 1--12).\N\NFor the entire collection see [Zbl 1539.11005].
scientific article; zbMATH DE number 7918583
scientific article