Results 1 to 10 of about 572,993 (300)

Multiple Argument Euler Sum Identities

Mathematics
We develop a number of new identities for linear Euler harmonic number sums with multiple argument. Some new examples of even weight linear Euler harmonic sum identities are given.
Anthony Sofo
doaj   +6 more sources

Simplex polynomial in complex networks and its applications to compute the Euler characteristic [PDF]

Frontiers in Computational Neuroscience
In algebraic topology, a k-dimensional simplex is defined as a convex polytope consisting of k + 1 vertices. If spatial dimensionality is not considered, it corresponds to the complete graph with k + 1 vertices in graph theory. The alternating sum of the
Zhaoyang Wang, Zhaoyang Wang, Xianghui Fu, Xianghui Fu, Bo Deng, Bo Deng, Yang Chen, Haixing Zhao, Haixing Zhao   +8 more
doaj   +2 more sources

Ordinary and degenerate Euler numbers and polynomials

Journal of Inequalities and Applications, 2019
In this paper, we study some identities on Euler numbers and polynomials, and those on degenerate Euler numbers and polynomials which are derived from the fermionic p-adic integrals on Zp $\mathbb{Z}_{p}$.
Taekyun Kim, Dae San Kim, Han Young Kim, Jongkyum Kwon   +3 more
doaj   +3 more sources

Odd Euler Sums and Harmonic Series with Cubic Central Binomial Coefficients in Denominators [PDF]

Axioms
By means of the coefficient extraction method, we examine a transformation of a classical hypergeometric series. Three classes of infinite series (of convergence rate “1/4”) with harmonic numbers in numerators and cubic central binomial coefficients in ...
Chunli Li, Wenchang Chu
doaj   +2 more sources

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
doaj   +1 more source

On generalized degenerate Euler–Genocchi polynomials

Applied Mathematics in Science and Engineering, 2023
We introduce the generalized degenerate Euler–Genocchi polynomials as a degenerate version of the Euler–Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler–Genocchi polynomials of order α ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
doaj   +1 more source

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
doaj   +1 more source

ON A SUM INVOLVING CERTAIN ARITHMETIC FUNCTIONS ON PIATETSKI–SHAPIRO AND BEATTY SEQUENCES

Проблемы анализа, 2022
Let 𝑐, 𝛼, 𝛽 ∈ R be such that ...
T. Srichan
doaj   +1 more source

Quantum Euler Relation for Local Measurements

Entropy, 2021
In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables.
Akram Touil, Kevin Weber, Sebastian Deffner   +2 more
doaj   +1 more source

Weighted and restricted sum formulas of Euler sums [PDF]

Research in Number Theory
Jianqiang Zhao
exaly   +2 more sources