After a short recall of the basic asymptotic relations “big O” and “small o”, we consider the Cauchy sums of the form ∑a≤k 0 ; in the case where α= 1 these are strictly related to the celebrated Riemann sums. After having learned how to approximate such sums, we apply the results to the approximation of sums of the form ∑0≤k
Cauchy and Riemann sums, factorials, Ramanujan numbers and their approximations
Mariconda C.;Tonolo A.
2016
Abstract
After a short recall of the basic asymptotic relations “big O” and “small o”, we consider the Cauchy sums of the form ∑a≤k 0 ; in the case where α= 1 these are strictly related to the celebrated Riemann sums. After having learned how to approximate such sums, we apply the results to the approximation of sums of the form ∑0≤k
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