Walter de Gruyter
We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have
and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have
Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers.
Available for download on Saturday, May 25, 2019