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In this paper, motivated by physical considerations, we introduce the notion of modified Riemann sums of Riemann-Stieltjes integrable functions, show that they converge, and compute them explicitely under various assumptions.
In this paper we investigate problems on almost everywhere convergence of subsequences of Riemann sums md0 R_nf(x)=frac{1}{n}sum_{k=0}^{n-1}fbigg(x+frac{k}{n}bigg),quad xin ZT. emd We establish a relevant connection between Riemann and ordinary maxim
We consider general formulations of the change of variable formula for the Riemann-Stieltjes integral, including the case when the substitution is not invertible.
We consider two integrals over $xin [0,1]$ involving products of the function $zeta_1(a,x)equiv zeta(a,x)-x^{-a}$, where $zeta(a,x)$ is the Hurwitz zeta function, given by $$int_0^1zeta_1(a,x)zeta_1(b,x),dxquadmbox{and}quad int_0^1zeta_1(a,x)zeta_1(b
We generalize Warnaars elliptic extension of a Macdonald multiparameter summation formula to Riemann surfaces of arbitrary genus.
Consider the Riemann sum of a smooth compactly supported function h(x) on a polyhedron in R^d, sampled at the points of the lattice Z^d/t. We give an asymptotic expansion when t goes to infinity, writing each coefficient of this expansion as a sum in