Results 11 to 20 of about 171,939 (293)
Evaluation of Euler-Zagier sums [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 We present a simple method for evaluation of multiple Euler sums in terms of single and double zeta values.
Khristo Boyadzhiev
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Mathematical Sciences, 2012 Continuing the studies started by \textit{D. H. Bailey} et al. [Exp. Math. 3, No. 1, 17--30 (1994; Zbl 0810.11076)] and refined by \textit{H. Chen} [J. Integer Seq. 9, No. 2, Article 06.2.3, 9 p. (2006; Zbl 1101.11033)], this paper develops a set of identities for Euler sums of the form \[ \sum^\infty_{n=1} \frac {H_{2n}}{n {n+k \choose k}} \] and its ...
Anthony Sofo, Sofo, Anthony
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An Euler-MacLaurin formula for polygonal sums [PDF]
Transactions of the American Mathematical Society, 2021 We prove an Euler-Maclaurin formula for double polygonal sums and, as a corollary, we obtain approximate quadrature formulas for integrals of smooth functions over polygons with integer vertices. Our Euler-Maclaurin formula is in the spirit of Pick's theorem on the number of integer points in an integer polygon and involves weighted Riemann sums, using
Brandolini, L +3 more
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Euler sums of hyperharmonic numbers
Journal of Number Theory, 2015 9 ...
Ayhan Dil, Khristo N. Boyadzhiev
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Generalization of the Flajolet Salvy identities for Euler Sums
Acta et Commentationes Universitatis Tartuensis de MathematicaThe exploration of linear Euler harmonic sums had its beginnings with the works of Euler in the 18th century. In 1998 Flajolet and Salvy published a seminal paper in which they developed an approach to the evaluation of linear Euler harmonic sums and gave explicit formulae for several classes of Euler sums in terms of Riemann zeta and other special ...
Sofo, Anthony
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Consecutive evaluation of Euler sums [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 We describe a simple method for a consecutive evaluation of the Euler sums S(r,p), r=1,2,… in terms of zeta values.
Khristo N. Boyadzhiev
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EULER-ZAGIER SUMS VIA TRIGONOMETRIC SERIES [PDF]
, 2023 In this note, we study the evaluations of Euler sums via trigonometric series. It is a commonly believed conjecture that for an even weight greater than seven, Euler sums cannot be evaluated in terms of the special values of the Riemann zeta function ...
Goral, Haydar, Celik, Sermin Cam
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Evaluation of Triple Euler Sums [PDF]
The Electronic Journal of Combinatorics, 1996 Let $a,b,c$ be positive integers and define the so-called triple, double and single Euler sums by $$\zeta(a,b,c) \ := \ \sum_{x=1}^{\infty} \sum_{y=1}^{x-1} \sum_{z=1}^{y-1} {1 \over x^a y^b z^c},$$ $$ \zeta(a,b) \ := \ \sum_{x=1}^\infty \sum_{y=1}^{x-1} {1 \over x^a y^b} \quad $$ and $$ \zeta(a) \ := \ \sum_{x=1}^\infty {1 \over x^a}.$$ Extending ...
Borwein, Jonathan M., Girgensohn, Roland
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Experimental Evaluation of Euler Sums [PDF]
Experimental Mathematics, 1994 In response to a letter from Goldbach, Euler considered sums of the form ∞ k=1 1+ 1 2 m + ··· + 1 k m (k +1 ) −n for positive integers m and n. Euler was able to give explicit values for certain of these sums in terms of the Riemann zeta function.
Bailey, David H. +2 more
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On q-analogues of quadratic Euler sums [PDF]
Periodica Mathematica Hungarica, 2020 In this paper we define the generalized q-analogues of Euler sums and present a new family of identities for q-analogues of Euler sums by using the method of Jackson q-integral rep- resentations of series. We then apply it to obtain a family of identities relating quadratic Euler sums to linear sums and q-polylogarithms.
Zhonghua Li, Ce Xu
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