Results 41 to 50 of about 2,037 (242)
New Approach to q-Euler Numbers and Polynomials
Advances in Difference Equations, 2010 We give a new construction of the q-extensions of Euler numbers and polynomials. We present new generating functions which are related to the q-Euler numbers and polynomials.
Seog-Hoon Rim +3 more
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A Note on Euler Numbers and Polynomials [PDF]
Nagoya Mathematical Journal, 1954 Let Em denote the Euler number in the even suffix notation so that(1.1) where, as usual, after expansion of the left member Er is replaced by Er. Nielsen [4, p. 273] has proved that(1.2)
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Euler characteristics and chromatic polynomials
European Journal of Combinatorics, 2007 This work studies the relation between the chromatic polynomial of a graph \(G\) and the Euler characteristic of certain spaces. These spaces are obtained by a construction which is a generalization of the configuration space. The authors show, in the case that \(G\) has only one point, the following theorem: Let \(G\) be a graph and \(M_G\) the ...
Michael Eastwood, Stephen Huggett
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Applied Mathematics in Science and EngineeringIn this work, we consider the degenerate Frobenius-Euler-Genocchi polynomials utilizing the degenerate exponential function and the degenerate Changhee-Frobenius-Euler-Genocchi polynomials utilizing the degenerate logarithm function.
Waseem Ahmad Khan +3 more
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On type 2 degenerate Bernoulli and Euler polynomials of complex variable
Advances in Difference Equations, 2019 Recently, Masjed-Jamei, Beyki, and Koepf studied the so-called new type Euler polynomials without using Euler polynomials of complex variable. Here we study the type 2 degenerate cosine-Euler and type 2 degenerate sine-Euler polynomials, which are type 2
Taekyun Kim +3 more
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Generalized -Euler Numbers and Polynomials Associated with -Adic -Integral on
International Journal of Mathematics and Mathematical Sciences, 2012 We generalize the Euler numbers and polynomials by the generalized -Euler numbers and polynomials . We observe an interesting phenomenon of “scattering” of the zeros of the generalized -Euler polynomials in complex plane.
H. Y. Lee +3 more
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On the Roots of Orthogonal Polynomials and Euler-Frobenius Polynomials
Journal of Mathematical Analysis and Applications, 1995 Consider a family of polynomials recursively defined by \(P_0 (x) = x^l\) \((l\) any nonnegative integer) and \[ c_{n + 1} P_{n + 1} (x) = - 2r_n xP_n (x) + (1 - x^2) P_n' (x), \quad n \geq 0, \] where \(r_n > 0\) and \(c_n \in \mathbb{R}\backslash\{0\}\). For example, ultraspherical and Euler-Frobenius polynomials verify this scheme.
Dubeau, F., Savoie, J.
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Umbral Calculus and the Frobenius-Euler Polynomials [PDF]
, 2013 We study some properties of umbral calculus related to the Appell sequence.
Dae San Kim, Sang-Hun Lee, Taekyun Kim
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Advanced Science, EarlyView.This study combines full‐field tomography with diffraction mapping to quantify radial (ε002$\varepsilon _{002}$) and axial (ε100$\varepsilon _{100}$) lattice strain in wrinkled carbon‐fiber specimens for the first time. Radial microstrain gradients (−14.5 µεMPa$\varepsilon \mathrm{MPa}$−1) are found to signal damage‐prone zones ahead of failure, which ...
Hoang Minh Luong +7 more
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Duals of the Bernoulli Numbers and Polynomials and the Euler Numbers and Polynomials
Integers, 2017 See the abstract in the attached pdf.
Tian-Xiao He, Jinze Zheng
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