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math.CA2025
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…
math.CA2025
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…
math.CA2024★ 3 cited
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…