Parametric euler sums of harmonic numbers
WebJul 11, 2024 · By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers, shifted harmonic numbers and Riemann zeta function with positive integer arguments. Web4 rows · Mar 21, 2024 · Abstract: We define a parametric variant of generalized Euler sums and construct contour ...
Parametric euler sums of harmonic numbers
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WebApr 21, 2010 · We extend some results of Euler related sums. Integral and closed-form representations of sums with products of harmonic numbers and binomial coefficients … WebMar 26, 2024 · The generalized harmonic numbers and the polygamma functions are related with \begin {aligned} H_n^ { (m)}=\zeta (m+1)+\frac { (-1)^m} {m!}\psi ^ { (m)} (n+1),\quad …
WebThe harmonic numbers roughly approximate the natural logarithm function [1] : 143 and thus the associated harmonic series grows without limit, albeit slowly. In 1737, Leonhard Euler …
WebEuler sums (values of multiple polylogarithms). REFERENCES ON MULTIPLE ZETA VALUES AND EULER SUMS Compiled by Michael Hoffman The list is in (approximate) chronological order within each category. generally tried to place each one in the most inclusive category that seemed appropriate. This list is revised regularly. [email protected]. Author index http://export.arxiv.org/abs/1701.03726
WebJan 3, 2024 · We establish some identities of Euler related sums. By using the identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial...
WebThe proof uses ideas from harmonic maps into the hyperbolic 3-space, WKB analysis, and the grafting of real projective structures. ... As there are only finitely many incompressible surfaces of bounded Euler characteristic up to isotopy in a hyperbolic 3-manifold, it makes sense to ask how the number of isotopy classes grows as a function of ... smith and wesson 38 special model 64-3WebIn a series of papers [7,30,31], the authors explore linear combinations of associated harmonic polylogarithms and nested harmonic numbers. The multiple zeta value data mine, computed by Blumlein et al. [ 32 ], is an invaluable tool for the evaluation of harmonic numbers, in which values with weights of twelve, for alternating sums, and weights ... smith and wesson 38 special pricingWebApr 13, 2024 · Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas - We confirm two conjectural congruences of Sun in Sun (Int J Math 26(8):1550055, 2015):... smith and wesson 38 special 5 shot revolverWeb(harmonic numbers) form a monotone sequence increasing without bound. The integral estimates 1 + 1 2 + :::+ 1 n > Z n+1 1 dx x = ln(n+ 1) and 1 2 + :::+ 1 n < Z n 1 dx x = lnn are justi ed geometrically. Combined together, they give ln(n+ 1) 1: Therefore H n tend to in nity at the same rate as lnn, which is fairly slow. For ... smith and wesson 38 special 4 inch barrelWebMar 21, 2024 · We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In … smith and wesson 38 snub nose revolver priceWebParametric Euler $T$-sums of odd harmonic numbers Ce Xu, Luhao Yan Mathematics 2024 In this paper, we define a parametric variant of generalized Euler sums and call them the (alternating) parametric Euler T -sums. By using the contour integration method and residue theorem, we… Expand 1 PDF View 1 excerpt, cites background Save Alert smith and wesson 38 snub nose revolver 5 shotWebFeb 6, 2024 · Recommend to Library Abstract In this paper, we deduce the asymptotic formulas of parametric digamma function Ψ ( − s; a) at the integers and poles. Then using these identities and residue theorem, we establish a large number of formulas of double series involving parametric harmonic numbers. smith and wesson 38 s\u0026w ctg revolver