Results 31 to 40 of about 2,224 (227)
Nonlinear Engineering, 2019 Herein, three important theorems were stated and proved. The first relates the modified generalized Laguerre expansion coefficients of the derivatives of a function in terms of its original expansion coefficients; and an explicit expression for the ...
Doha E.H., Youssri Y.H.
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Construction of partially degenerate Laguerre-Genocchi polynomials with their applications
AIMS Mathematics, 2020 Various applications of degenerate polynomials in different areas call for the thoughtful study and research, and many extensions and variants can be found in the literature.
Talha Usman +4 more
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Abstract and Applied Analysis, 2013 This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line.
D. Baleanu, A. H. Bhrawy, T. M. Taha
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Inequalities for Laguerre functions
Journal of Inequalities and Applications, 1997 The main published inequality for Laguerre functions Lvμ(z) seems to be for Laguerre polynomials Ln0(x) only; it is [2: 10.18(3)]: |Ln(x)|≤ex/2  for  x>0.This paper presents several inequalities for Laguerre polynomials Lnμ(x) and ...
E. R. Love
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Bispectral Laguerre type polynomials [PDF]
Integral Transforms and Special Functions, 2019 We study the bispectrality of Laguerre type polynomials, which are defined by taking suitable linear combinations of a fixed number of consecutive Laguerre polynomials. These Laguerre type polynomials are eigenfunctions of higher-order differential operators and include, as particular cases, the Krall-Laguerre polynomials. As the main results, we prove
Antonio J. Durán +1 more
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MathematicsThis paper presents a novel generalization of the mth-order Laguerre and Laguerre-based Appell polynomials and examines their fundamental properties. By establishing quasi-monomiality, we derive key results, including recurrence relations, multiplicative
Waseem Ahmad Khan +4 more
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Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces
Mathematics, 2021 Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials.
Pedro J. Miana, Natalia Romero
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On Appell-Laguerre polynomials
Journal of Computational and Applied Mathematics, 1993 AbstractIn this note we give a digest study of Appell-Laguerre polynomials, we provide a recurrence relation and a second-order differential equation satisfied by these polynomials. Moreover, an explicit expression and a generating function of the polynomials are given.
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Some Identities on Laguerre Polynomials in Connection with Bernoulli and Euler Numbers
Discrete Dynamics in Nature and Society, 2012 We study some interesting identities and properties of Laguerre polynomials in connection with Bernoulli and Euler numbers. These identities are derived from the orthogonality of Laguerre polynomials with respect to inner product ∫⟨𝑓,𝑔⟩=∞0𝑒−𝑥2𝑓(𝑥)𝑔(𝑥)𝑑𝑥.
Dae San Kim +2 more
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Generalizations of Laguerre polynomials
Journal of Mathematical Analysis and Applications, 1990 AbstractIt is shown that the polynomials {Lnα,M0,M1,…,MN(x)}n = 0∞ defined by Lnα,M0M1,…,MN(x)=∑k=0N+1Ak·DkLn(α)(x) for certain real coefficients {Ak}k = 0N + 1 are orthogonal with respect to the inner product 〈f,g〉=1Γ(α+1)·∫0∞xαe−x·f(x)g(x)dx+∑v=0NMv·f(v)(0)g(v)(0), where α > − 1, N ϵ N and Mv ⩾ 0 for all v ϵ {0, 1, 2, …, N}. For these new polynomials
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