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Euler Sums and Integral Connections
Mathematics, 2019 In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler’s work on the subject followed by notations used in the body of the paper.
Amrik Nimbran, Anthony Sofo
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Some identities and reciprocity relationsof unipoly-Dedekind type DC sums
Journal of Inequalities and Applications, 2021 Dedekind type DC sums and their generalizations are defined in terms of Euler functions and their generalization. Recently, Ma et al. (Adv. Differ. Equ. 2021:30 2021) introduced the poly-Dedekind type DC sums by replacing the Euler function appearing in ...
Hye Kyung Kim, Dae Sik Lee
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Dirichlet type extensions of Euler sums
Comptes Rendus. Mathématique, 2023 In this paper, we study the alternating Euler $T$-sums and $\tilde{S}$-sums, which are infinite series involving (alternating) odd harmonic numbers, and have similar forms and close relations to the Dirichlet beta functions.
Xu, Ce, Wang, Weiping
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Reciprocity of poly-Dedekind-type DC sums involving poly-Euler functions
Advances in Difference Equations, 2021 The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group.
Yuankui Ma +4 more
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Reciprocity of degenerate poly-Dedekind-type DC sums
Applied Mathematics in Science and Engineering, 2023 Dedekind-type DC sums and their properties are defined in terms of Euler functions. Ma et al. recently introduced poly-Dedekind-type DC sums and demonstrated that they satisfy a reciprocity relation.
Lingling Luo +3 more
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Euler-type sums involving multiple harmonic sums and binomial coefficients
Open Mathematics, 2021 In this paper, we mainly show that generalized Euler-type sums of multiple harmonic sums with reciprocal binomial coefficients can be expressed in terms of rational linear combinations of products of classical multiple zeta values (MZVs) and multiple ...
Si Xin
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Evaluating log-tangent integrals via Euler sums
Mathematical Modelling and Analysis, 2022 An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper.
Anthony Sofo
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Is Catalan’s Constant Rational?
Mathematics, 2022 This paper employs a contour integral method to derive and evaluate the infinite sum of the Euler polynomial expressed in terms of the Hurwitz Zeta function. We provide formulae for several classes of infinite sums of the Euler polynomial in terms of the
Robert Reynolds, Allan Stauffer
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A note on type 2 q-Bernoulli and type 2 q-Euler polynomials
Journal of Inequalities and Applications, 2019 As is well known, power sums of consecutive nonnegative integers can be expressed in terms of Bernoulli polynomials. Also, it is well known that alternating power sums of consecutive nonnegative integers can be represented by Euler polynomials.
Dae San Kim +3 more
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Approximation of functions in Hölder’s class and solution of nonlinear Lane–Emden differential equation by orthonormal Euler wavelets [PDF]
Iranian Journal of Numerical Analysis and OptimizationIn this article, a method has been developed for the solution of a non-linear Lane-Emden differential equation based on orthonormal Euler wavelet series.
H.C. Yadav, A. Yadav, S. Lal
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