8 papers
New central -binomial identities
Shane Chern, Karl Dilcher, Lin Jiu
We establish several new series evaluations involving the central -binomial coefficients, with the inspiration coming from earlier work by Vignat and one of the authors on the l…
Properties of two Chebyshev-like polynomial sequences
Karl Dilcher, Seon-Hong Kim, Kenneth B. Stolarsky
By modifying the generating function of the Chebyshev polynomials of the second kind, we obtain a sequence of reciprocal (or palindromic) polynomials, as well as a related companio…
Integrals involving arbitrary powers of the arcsine, with applications to infinite series
Karl Dilcher, Christophe Vignat
Using appropriate power series evaluations, we determine all moments of arbitrary positive powers of the arcsine. As consequences we evaluate several doubly infinite classes of pow…
Powers of the arcsine and infinite classes of series involving central binomial coefficients
Karl Dilcher, Christophe Vignat
A general integral expression to transform power series is applied to and its positive integer powers. We concentrate on the first to the fourth powers and obtain infi…
Further Classes of Series Involving Central Binomial Coefficients
Karl Dilcher, Christophe Vignat
Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all…
An alternating sum of the floor function of square roots
Marc Chamberland, Karl Dilcher
We show that the alternating sum of the floor function of , with ranging from 1 to , has an easy evaluation for all odd integers . This is in contrast to…