Results 41 to 50 of about 68,130 (264)
Some Identities of the Frobenius‐Euler Polynomials [PDF]
Abstract and Applied Analysis, 2009 By using the ordinary fermionic p‐adic invariant integral on ℤp, we derive some interesting identities related to the Frobenius‐Euler polynomials.
Kim, Taekyun, Lee, Byungje
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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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Hard‐Magnetic Soft Millirobots in Underactuated Systems
Advanced Robotics Research, EarlyView.This review provides a comprehensive overview of hard‐magnetic soft millirobots in underactuated systems. It examines key advances in structural design, physics‐informed modeling, and control strategies, while highlighting the interplay among these domains.
Qiong Wang +4 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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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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Multiple Twisted q-Euler Numbers and Polynomials Associated with p-Adic q-Integrals
Advances in Difference Equations, 2008 By using p-adic q-integrals on ℤp, we define multiple twisted q-Euler numbers and polynomials. We also find Witt's type formula for multiple twisted q-Euler numbers and discuss some characterizations of multiple twisted q-Euler Zeta functions.
Lee-Chae Jang
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Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials
Advances in Difference Equations, 2020 The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation.
Alejandro Urieles +3 more
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A note on q-Euler numbers and polynomials
, 2006 The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 ...
A. S. Hegazi +20 more
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Derivative Polynomials, Euler Polynomials, and Associated Integer Sequences [PDF]
The Electronic Journal of Combinatorics, 1999 Let $P_n$ and $Q_n$ be the polynomials obtained by repeated differentiation of the tangent and secant functions respectively. From the exponential generating functions of these polynomials we develop relations among their values, which are then applied to various numerical sequences which occur as values of the $P_n$ and $Q_n$.
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