Euler Sums and Integral Connections

Sofo, Anthony; Nimbran, Amrik Singh

doi:10.3390/math7090833

Cited by 17 publications

(12 citation statements)

References 33 publications

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“…The second of the sums appearing in ( 26) can be found by substituting z = i into the generating function given in Lemma 4.6. Doing so we have after substituting in the values found in ( 33), ( 34), ( 35), ( 36), ( 37), (38), and (45). Further reduction here has been possible since the sum between the two tetralogarithmic terms that appeared, namely…”

Section: Seán M Stewartmentioning

confidence: 99%

Explicit Evaluation of Some Quadratic Euler-Type Sums Containing Double-Index Harmonic Numbers

Stewart¹

2020

Tatra Mountains Mathematical Publications

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In this paper a number of new explicit expressions for quadratic Euler-type sums containing double-index harmonic numbers H2n are given. These are obtained using ordinary generating functions containing the square of the harmonic numbers Hn. As a by-product of the generating function approach used new proofs for the remarkable quadratic series of Au-Yeung \sum\limits_{n = 1}^\infty {{{\left( {{{{H_n}} \over n}} \right)}^2} = {{17{\pi ^4}} \over {360}}} together with its closely related alternating cousin are given. New proofs for other closely related quadratic Euler-type sums that are known in the literature are also obtained.

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Section: Seán M Stewartmentioning

confidence: 99%

Explicit Evaluation of Some Quadratic Euler-Type Sums Containing Double-Index Harmonic Numbers

Stewart¹

2020

Tatra Mountains Mathematical Publications

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“…The identity (1.12) is a particular instance of the following more generalized Euler sum (see, e.g., [6], [9], [11], [20]):…”

Section: Et Seq])mentioning

confidence: 99%

Four types of variant Euler harmonic sums

Batır¹,

Choi²

2023

Preprint

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We aim to investigate the four types of variant Euler harmonic sums. Also, as corollaries, we provide particular examples of our core findings, some of whose further instances are evaluated in terms of basic and well-known functions as well as certain mathematical constants. We explore relevant linkages between our results and those of other previously established studies. An examination of a specific case of one result shows a relationship to series involving zeta functions, which is also a popular area of research.

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“…A search of the current literature has found some examples for the representation of the log-log integrals in terms of Euler sums, see [27]. The following papers [11,[18][19][20][21] and [22] also examined some integrals in terms of Euler sums. The two examples (1.2) and (1.3) will be considered in detail, moreover, these integrals are not amenable to a computer mathematical package.…”

Section: > < > :mentioning

confidence: 99%