Generalizations of Knopp's Identity

AbstractFor integers a, b and n > 0 we define SΓ(a,b,n) = ∑r=0n∤brn−1arn ln Γbrn andSΓ(a,b,n) = ∑r=0r=0n∤brn−1arnΓ′({br/n})Γ({br/n}) which are similar to the homogeneous Dedekind sum S(a,b,n). In this paper we establish functional equations for SΓ and TΓ. Moreover, by means of uniform function (introduced by Sun in 1989) we are able to extend Knopp's identity on Dedekind sums vastly