Modular relations involving generalized digamma functions (Q6614327)

Let \(\psi_{k}(x)\) denotes the generalized digamma functions.\N\NIn this paper under review, the authors obtained modular relation of the form \(F_{k}(z) = F_{k}(1/z)\) containing infinite series of \(\psi_{k}(x)\) for any \(k\in{\mathbb{N}}\). Their results extend previous results on the digamma function \(\psi(x)\). Other results are obtained, for example, they extended Guinand's result for \(\psi^{m}_{j}(x),\ m \geq2\), involves an interesting combinatorial sum \(h(r)\) over integer partitions of \(2r\) into exactly \(r\) parts.