Results 31 to 40 of about 46,179 (201)
Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 Let Pn = {p(x) ∈ ℝ[x]∣deg p(x) ≤ n} be an inner product space with the inner product , where p(x), q(x) ∈ Pn and α ∈ ℝ with α > −1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis for Pn.
Kim, Taekyun, Kim, Dae San
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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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Some Properties on the q‐Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 We give some new identities on q‐Euler numbers and polynomials by using the fermionic p‐adic integral on ℤp.
Kim, T., Lee, S.-H.
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Explicit formulas for Euler polynomials and Bernoulli numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In this paper, we give several explicit formulas involving the n-th Euler polynomial E_{n}\left(x\right). For any fixed integer m\geq n, the obtained formulas follow by proving that E_{n}\left(x\right) can be written as a linear combination of the polynomials x^{n}, \left(x+r\right)^{n},\ldots, \left(x+rm\right)^{n}, with r\in \left \{1,-1,\frac{1}{2 ...
Laala Khaldi +2 more
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A note on Euler number and polynomials [PDF]
Journal of Inequalities and Applications, 2006 The multiple Euler polynomials of \(p\)-adic arguments are defined via a \(p\)-adic integration procedure proposed by \textit{T. Kim} [J. Number Theory 76, No. 2, 320--329 (1999; Zbl 0941.11048)]. The authors give a formula for a sum of products of Euler polynomials. This answers a question by \textit{I.-C. Huang} and \textit{S.-Y. Huang} [J.
Kim Seoung-Dong +3 more
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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
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A note on the q-Genocchi numbers and polynomials [PDF]
, 2007 In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.Comment: 8 ...
Kim, Taekyun
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Sums of Products of Kronecker's Double Series [PDF]
, 2006 Closed expressions are obtained for sums of products of Kronecker's double series. Corresponding results are derived for functions which are an elliptic analogue of the periodic Euler polynomials.
Machide, Tomoya
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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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Stirling Numbers and Spin-Euler Polynomials [PDF]
Experimental Mathematics, 2007 The Fischer decomposition on ℝn gives the decomposition of arbitrary homogeneous polynomials in n variables (x 1, . . . , x n) in terms of harmonic homogeneous polynomials. In classical Clifford analysis a refinement was obtained, giving a decomposition in terms of monogenic polynomials, i.e., homogeneous null solutions for the Dirac operator (a vector-
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