Results 21 to 30 of about 6,793 (328)
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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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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Coccolith arrangement follows Eulerian mathematics in the coccolithophore Emiliania huxleyi [PDF]
PeerJ, 2018 Background The globally abundant coccolithophore, Emiliania huxleyi, plays an important ecological role in oceanic carbon biogeochemistry by forming a cellular covering of plate-like CaCO3 crystals (coccoliths) and fixing CO2. It is unknown how the cells
Kai Xu, David Hutchins, Kunshan Gao
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General Euler-Boole's and dual Euler-Boole's formulae [PDF]
Mathematical Inequalities & Applications, 2005 The aim of this talk is to give general Euler-Boole's and dual Euler-Boole's formulae. More precisely, we derive formulae of Boole type where the integral is approximated not only with the values of the function in certain points but also with values of its derivatives up to (2n-1)-th order in end points of the interval. Our method produces formulae of
Pečarić, Josip +2 more
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On the degrees of freedom of lattice electrodynamics [PDF]
, 2005 Using Euler's formula for a network of polygons for 2D case (or polyhedra for 3D case), we show that the number of dynamic\textit{\}degrees of freedom of the electric field equals the number of dynamic degrees of freedom of the magnetic field for ...
Adams +22 more
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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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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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Complex Numbers Related to Semi-Antinorms, Ellipses or Matrix Homogeneous Functionals
Axioms, 2021 We generalize the property of complex numbers to be closely related to Euclidean circles by constructing new classes of complex numbers which in an analogous sense are closely related to semi-antinorm circles, ellipses, or functionals which are ...
Wolf-Dieter Richter
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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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, 2002 In q-calculus, the Jackson formula (19.2) provides a way to compute explicitly a q-antiderivative of any function. Recall that the Jackson formula was deduced formally using operators. We will do a similar thing for the h-antiderivative in this chapter.
Victor Kac, Pokman Cheung
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