4 citations · 7 across the 21 of their papers we have counts for
4 papers · 2 filters
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…
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…
Sums of the floor function related to class numbers of imaginary quadratic fields
Marc Chamberland, Karl Dilcher
A curious identity of Bunyakovsky (1882), made more widely known by Pólya and Szeg{\H o} in their ``Problems and Theorems in Analysis", gives an evaluation of a sum of the floor fu…