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math.NT2025
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…
math.NT2025
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…