Results 11 to 20 of about 32,087 (238)
K-regular decomposable incidence structure of maximum degree [PDF]
Mathematica Moravica, 2023 This paper discusses incidence structures and their rank. The aim of this paper is to prove that there exists a regular decomposable incidence structure J = (P, B) of maximum degree depending on the size of the set and a predetermined rank.
Stošović Dejan +2 more
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Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x) [PDF]
, 2010 We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial ...
Miller, A. R., Paris, Richard B.
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A note on hyperbolic quaternions
Universal Journal of Mathematics and Applications, 2018 In this work, we introduce hyperbolic quaternions and their algebraic properties. Moreover, we express Euler's and De Moivre's formulas for hyperbolic quaternions.
İşıl Arda Kösal
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A simple proof of generalizations of number-theoretic sums [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron +1 more
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A q-analog of Euler's decomposition formula for the double zeta function [PDF]
, 2005 The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum
Bradley, David M.
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The Desymmetrized PSL(2, Z) Group; Its ‘Square-Box’ One-Cusp Congruence Subgroups
Computer Sciences & Mathematics Forum, 2023 In this paper, the desymmetrized PSL(2, Z) group is studied. The Fourier coefficients of the non-holomorphic one-cusp Eisenstein series expansion are summed, and as a further result, a new dependence on the Euler’s γ constant is found.
Orchidea Maria Lecian
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Analogues of Euler and Poisson summation formulae [PDF]
, 2002 Euler--Maclaurin and Poisson analogues of the summations $\sum_{a < n \leq b} \chi(n) f(n)$, $\sum_{a < n \leq b} d(n) f(n)$, $\sum_{a < n \leq b} d(n) \chi (n) f(n)$ have been obtained in a unified manner, where $(\chi (n))$ is a periodic complex ...
Rane, Vivek V
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Unification Theories: Means and Generalized Euler Formulas
Axioms, 2020 The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized.
Radu Iordanescu +2 more
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An Examination of Counterexamples in Proofs and Refutations
Philosophia Scientiæ, 2009 : Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra.
Samet Bağçe, Can Başkent
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On a generalization of Euler's constant [PDF]
Surveys in Mathematics and its Applications, 2021 A one parameter generalization of Euler's constant γ from [Numer. Algorithms 46(2) (2007) 141--151] is investigated, and additional expressions for γ are derived.
Stephen Kaczkowski
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