3 papers
math.NT2019
Hypergeometric rational approximations to
Raffaele Marcovecchio, Wadim Zudilin
We give a new hypergeometric construction of rational approximations to , which absorbs the earlier one from 2003 based on Bailey's hypergeometric integrals. With t…
math.CV2019
A classical functional generalization of the first Barnes lemma
Raffaele Marcovecchio
We give a brief account and a simpler proof of a contour integral formula for the Gauss hypergeometric function. Such formula is alternative to Barnes's integral formula and genera…
math.NT2018
Some remarks in elementary prime number theory
Raffaele Marcovecchio
We give an outline of a generalization of the Gelfond-Schnirelmann method in elementary number theory. It is related to an integral of Selberg (1944) generalizing the Euler beta in…