61 citations · 71 across the 8 of their papers we have counts for
8 papers
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…
Exploring Integration by Differentiation
R. D. George, C. Vignat
This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of in…
Berndt-type Integrals: Unveiling Connections with Barnes Zeta and Jacobi Elliptic Functions
Zachary P. Bradshaw, Christophe Vignat
We address a class of definite integrals known as Berndt-type integrals, highlighting their role as specialized instances within the integral representation framework of the Barnes…
General Convolution Identities for Bernoulli and Euler Polynomials
K. Dilcher, C. Vignat
Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k \ge 2) conv…