General order Euler sums with multiple argument
For positive integers \(k,m,p\) let \[ T(k,m,p)=\sum_{n=1}^\infty\frac{H_{pn}^{(m)}}{n}\frac{n+k}{k}. \] In the paper under review the author develops analytic representations for \(T(k,m,p)\) in terms of the the Riemann zeta-function \(\zeta(m)\) and a weighted integral involving hypergeometric function \(_2F_1\). As some examples, the author considers special cases connected with well-known constants. Also, for \(k\geq 2\) he obtains bounds for \(T(k,m,p)\) in terms of polygamma function.
scientific article; zbMATH DE number 6865887
scientific article