Relevant bibliographies by topics / Laguerre polynomial

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Laguerre polynomial'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Laguerre polynomial"

1

Jagtap, R. R., P. G. Andhare та S. B. Gaikwad. "A New General Integral Transform of Modified Laguerre’s Polynomial 𝐿𝐚,𝐛,𝐜,𝐧(𝑡)". Indian Journal Of Science And Technology 17, № 39 (2024): 4066–72. http://dx.doi.org/10.17485/ijst/v17i39.1251.

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Objectives: The core objective of this paper is to introduce the explicit Modified Laguerre polynomial 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡) and obtain a new general integral transform of Modified Laguerre’s Polynomial, by using this general transform, some transforms of Laguerre’s Polynomial are identified as special cases. Method: We derive transforms of the polynomials 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡), 𝐿𝑛 (𝑡) by using this new integral transform approach and found the transforms like Laplace, 𝛼-Laplace, Sawi, Elzaki, Sumudu, Natural, Aboodh, Pourreza, Mohand, G_transform, Kamal transforms and their relationship for the same. Findings:
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R, R. Jagtap, G. Andhare P та B. Gaikwad S. "A New General Integral Transform of Modified Laguerre's Polynomial 𝐿𝐚,𝐛,𝐜,𝐧(𝑡)". Indian Journal of Science and Technology 17, № 39 (2024): 4066–72. https://doi.org/10.17485/IJST/v17i39.1251.

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Abstract <strong>Objectives:</strong>&nbsp;The core objective of this paper is to introduce the explicit Modified Laguerre polynomial 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡) and obtain a new general integral transform of Modified Laguerre&rsquo;s Polynomial, by using this general transform, some transforms of Laguerre&rsquo;s Polynomial are identified as special cases.&nbsp;<strong>Method:</strong>&nbsp;We derive transforms of the polynomials 𝐿𝑎,𝑏,𝑐,𝑛 (𝑡), 𝐿𝑛 (𝑡) by using this new integral transform approach and found the transforms like Laplace, 𝛼-Laplace, Sawi, Elzaki, Sumudu, Natural, Aboodh, Pourreza, Mohand, G_tran
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Alam, Noor, Shahid Ahmad Wani, Waseem Ahmad Khan, Fakhredine Gassem та Anas Altaleb. "Exploring Properties and Applications of Laguerre Special Polynomials Involving the Δh Form". Symmetry 16, № 9 (2024): 1154. http://dx.doi.org/10.3390/sym16091154.

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The primary objective of this research is to introduce and investigate novel polynomial variants termed Δh Laguerre polynomials. This unique polynomial type integrates the monomiality principle alongside operational rules. Through this innovative approach, the study delves into uncharted territory, unveiling fresh insights that build upon prior research endeavours. Notably, the Δh Laguerre polynomials exhibit significant utility in the realm of quantum mechanics, particularly in the modelling of entropy within quantum systems. The research meticulously unveils explicit formulas and elucidates
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DUNKL, CHARLES F. "A LAGUERRE POLYNOMIAL ORTHOGONALITY AND THE HYDROGEN ATOM." Analysis and Applications 01, no. 02 (2003): 177–88. http://dx.doi.org/10.1142/s0219530503000132.

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The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis, an analogous strange orthogonality is obtained for Meixner polynomials.
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Khan, Adnan, Muhammad Kalim, Ali Akgül та Fahd Jarad. "The Extended Laguerre Polynomials A q , n α x Involving F q q , q > 2". Journal of Function Spaces 2022 (15 квітня 2022): 1–14. http://dx.doi.org/10.1155/2022/7326760.

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In this paper, for the proposed extended Laguerre polynomials A α q , n x , the generalized hypergeometric function of the type F q q , q &gt; 2 and extension of the Laguerre polynomial are introduced. Similar to those related to the Laguerre polynomials, the generating function, recurrence relations, and Rodrigue’s formula are determined. Some corollaries are also discussed at the end.
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Blel, Mongi. "On some m-symmetric generalized hypergeometric d-orthogonal polynomials." Filomat 38, no. 4 (2024): 1279–89. http://dx.doi.org/10.2298/fil2404279b.

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In [9] I. Lamiri and M. Ouni state some characterization theorems for d-orthogonal polynomials of Hermite, Gould-Hopper and Charlier type polynomials. In [3] Y. Ben Cheikh I. Lamiri and M.Ouni give a characterization theorem for some classes of generalized hypergeometric polynomials containing for example, Gegenbauer polynomials, Gould-Hopper polynomials, Humbert polynomials, a generalization of Laguerre polynomials and a generalization of Charlier polynomials. In this work, we introduce a new class D of generalized hypergeometric m-symmetric polynomial sequence containing the Hermite polynomi
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Hajmirzaahmad, Mojdeh. "Laguerre polynomial expansions." Journal of Computational and Applied Mathematics 59, no. 1 (1995): 25–37. http://dx.doi.org/10.1016/0377-0427(94)00020-2.

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Asad, A. "Two variables generalized Laguerre polynomials." Carpathian Mathematical Publications 13, no. 1 (2021): 134–41. http://dx.doi.org/10.15330/cmp.13.1.134-141.

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The objective of this paper is to introduce and study the generalized Laguerre polynomial for two variables. We prove that these polynomials are characterized by the generalized hypergeometric function. An explicit representation, generating functions and some recurrence relations are shown. Moreover, these polynomials appear as solutions of some differential equations.
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Khan, Adnan, M. Haris Mateen, Ali Akgül та Md Shajib Ali. "The K Extended Laguerre Polynomials Involving A α r , n , k x F r r , r > 2". Advances in Mathematical Physics 2022 (5 вересня 2022): 1–10. http://dx.doi.org/10.1155/2022/6815685.

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In this manuscript, we present the generalized hypergeometric function of the type F r r , r &gt; 2 and extension of the K Laguerre polynomial for the K extended Laguerre polynomials A r , n , k α x . Additionally, we describe the K generating function, K recurrence relations, and K S Rodrigues formula.
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Baleanu, D., A. H. Bhrawy, and T. M. Taha. "A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/413529.

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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. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method.
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Dissertations / Theses on the topic "Laguerre polynomial"

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Barros, Michele Carvalho de. "Comportamento assintótico dos polinômios ortogonais de Sobolev-Jacobi e Sobolev-Laguerre /." São José do Rio Preto : [s.n.], 2008. http://hdl.handle.net/11449/94284.

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Orientador: Eliana Xavier Linhares de Andrade<br>Banca: Ana Paula Peron<br>Banca: Alagacone Sri Ranga<br>Resumo: Sejam Sn(x); n ¸ 0; os polinômios de Sobolev, ortogonais com relação ao produto interno hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; onde fdÃ0; dÃ1g forma um par coerente de medidas relacionadas às medidas de Jacobi ou de Laguerre. Denotemos por PÃ0 n (x) e PÃ1 n (x); n ¸ 0; os polinômios ortogonais com respeito a dÃ0 e dÃ1; respectivamente. Neste trabalho, estudamos o comportamento assintótico, quando n ! 1; das razões entre os polinômios de Sobolev, Sn(x); e os poli
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Barros, Michele Carvalho de [UNESP]. "Comportamento assintótico dos polinômios ortogonais de Sobolev-Jacobi e Sobolev-Laguerre." Universidade Estadual Paulista (UNESP), 2008. http://hdl.handle.net/11449/94284.

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Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-25Bitstream added on 2014-06-13T19:06:37Z : No. of bitstreams: 1 barros_mc_me_sjrp.pdf: 547514 bytes, checksum: eb85ffc4b82cf33a3b73f60814c6355f (MD5)<br>Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)<br>Sejam Sn(x); n ¸ 0; os polinômios de Sobolev, ortogonais com relação ao produto interno hf; giS = ZR f(x)g(x)dÃ0(x) + ¸ ZR f0(x)g0(x)dÃ1(x); ¸ > 0; onde fdÃ0; dÃ1g forma um par coerente de medidas relacionadas às medidas de Jacobi ou de Laguerre. Denotemos por PÃ0 n
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Guerfi, Malik. "Les polynômes de Laguerre-Hahn affines discrets." Paris 6, 1988. http://www.theses.fr/1988PA066275.

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On montre que les polynômes semiclassiques sont des polynômes de Laguerre-Hahn affines et réciproquement. On étudie les polynômes corécursifs et les polynômes associés des polynômes de Laguerre Hahn affines. On généralise tous ces résultats aux polynômes semiclassiques discrets (avec l'opérateur de Hahn)
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Dini, Jamal. "Sur les formes linéaires et les polynômes orthogonaux de Laguerre-Hann." Paris 6, 1988. http://www.theses.fr/1988PA066201.

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Le caractere semi-classique ou laguerre-hahn d'une forme lineaire reguliere reste stable par la multiplication par un polynome ou par adjonction d'une masse de dirac. La suite associee d'une suite de polynomes semi-classiques est de laguerre-hahn. Ces diverses operations permettent de generer d'autres suites orthogonales dont on etudie les proprietes. On donne aussi diverses caracterisations des polynomes de laguerre-hahn
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Tůma, Martin. "Použití zobecněných Laguerrových funkcí pro identifikaci a modelování." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-316736.

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Tato práce se zabývá použitím zobecněných Laguerrových funkcí pro modelování a identifikaci dynamických systémů. Po krátkém úvodu je uvedena definice zobecněných Laguerrových polynomů a funkcí a některé jejich vlastnosti. Je zavedena metoda pro identifikaci spojitých dynamických systémů z diskrétních nasamplovaných dat s použitím zobecněných Laguerrových funkcí a porovnána s metodou nejmenších čtverců. Je diskutována volba optimálních parametrů p a alpha pro konečné Fourierovy řady se zobecněnými Laguerrovými funkcemi. Na příkladech je porovnána navržená identifikační metoda s metodou nejmenší
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Ottergren, Elin. "Multiplier Sequences for Laguerre bases." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-83391.

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Pólya and Schur completely characterized all real-rootedness preserving linear operators acting on the standard monomial basis in their famous work from 1914. The corresponding eigenvalues are from then on known as multiplier sequences. In 2009 Borcea and Br\"and\'en gave a complete characterization for general linear operators preserving real-rootedness (and stability) via the symbol. Relying heavily on these results, in this thesis, we are able to completely characterize multiplier sequences for generalized Laguerre bases. We also apply our methods to reprove the characterization of Hermite
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Tipton, Earl Lynn Loyalka S. K. Tompson R. V. "Chapman-Enskog solutions to arbitrary order in Sonine polynomials." Diss., Columbia, Mo. : University of Missouri--Columbia, 2008. http://hdl.handle.net/10355/7192.

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Title from PDF of title page (University of Missouri--Columbia, viewed on February 23, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Sudarshan K. Loyalka and Dr. Robert V. Tompson. Vita. Includes bibliographical references.
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Marumo, Kohei. "Expansion methods applied to distributions and risk measurement in financial markets." Thesis, Queensland University of Technology, 2007. https://eprints.qut.edu.au/16506/1/Kohei_Marumo_Thesis.pdf.

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Obtaining the distribution of the profit and loss (PL) of a portfolio is a key problem in market risk measurement. However, existing methods, such as those based on the Normal distribution, and historical simulation methods, which use empirical distribution of risk factors, face difficulties in dealing with at least one of the following three problems: describing the distributional properties of risk factors appropriately (description problem); deriving distributions of risk factors with time horizon longer than one day (time aggregation problem); and deriving the distribution of the PL given
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Marumo, Kohei. "Expansion methods applied to distributions and risk measurement in financial markets." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16506/.

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Obtaining the distribution of the profit and loss (PL) of a portfolio is a key problem in market risk measurement. However, existing methods, such as those based on the Normal distribution, and historical simulation methods, which use empirical distribution of risk factors, face difficulties in dealing with at least one of the following three problems: describing the distributional properties of risk factors appropriately (description problem); deriving distributions of risk factors with time horizon longer than one day (time aggregation problem); and deriving the distribution of the PL given
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Kasraoui, Anisse. "Études combinatoires sur les permutations et partitions d'ensemble." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00393631.

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Cette thèse regroupe plusieurs travaux de combinatoire énumérative sur les permutations et permutations d'ensemble. Elle comporte 4 parties.Dans la première partie, nous répondons aux conjectures de Steingrimsson sur les partitions ordonnées d'ensemble. Plus précisément, nous montrons que les statistiques de Steingrimsson sur les partitions ordonnées d'ensemble ont la distribution euler-mahonienne. Dans la deuxième partie, nous introduisons et étudions une nouvelle classe de statistiques sur les mots : les statistiques "maj-inv". Ces dernières sont des interpolations graphiques des célèbres st
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Books on the topic "Laguerre polynomial"

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Funaro, Daniele. Computational aspects of pseudospectral Laguerre approximations. Institute for Computer Applications in Science and Engineering, 1989.

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Funaro, Daniele. Computational aspects of pseudospectral Laguerre approximations. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Funaro, Daniele. Computational aspects of pseudospectral Laguerre approximations. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Dyson, Freeman. Spectral statistics of unitary ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.4.

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This article focuses on the use of the orthogonal polynomial method for computing correlation functions, cluster functions, gap probability, Janossy density, and spacing distributions for the eigenvalues of matrix ensembles with unitary-invariant probability law. It first considers the classical families of orthogonal polynomials (Hermite, Laguerre, and Jacobi) and some corresponding unitary ensembles before discussing the statistical properties of N-tuples of real numbers. It then reviews the definitions of basic statistical quantities and demonstrates how their distributions can be made expl
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Odeniran, Ayo. On Zeros of Laguerre Polynomials. GRIN Verlag GmbH, 2016.

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Anderson, Greg W. Spectral statistics of orthogonal and symplectic ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.5.

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This article describes a direct approach for computing scalar and matrix kernels, respectively for the unitary ensembles on the one hand and the orthogonal and symplectic ensembles on the other hand, leading to correlation functions and gap probabilities. In the classical orthogonal polynomials (Hermite, Laguerre, and Jacobi), the matrix kernels for the orthogonal and symplectic ensemble are expressed in terms of the scalar kernel for the unitary case, using the relation between the classical orthogonal polynomials going with the unitary ensembles and the skew-orthogonal polynomials going with
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I, Krylov V., V. S. Aizenshtadt, and A. S. Metel'skii. Tables of Laguerre Polynomials and Functions: Mathematical Tables Series, Vol. 39. Elsevier Science & Technology Books, 2014.

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Polynomes Orthogonaux et Applications: Proceedings of the Laguerre Symposium held at Bar-le-Duc, October 15-18, 1984 (Lecture Notes in Mathematics) (English, French and German Edition). Springer, 1985.

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Book chapters on the topic "Laguerre polynomial"

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Zhang, Yunong, Dechao Chen, and Chengxu Ye. "Single-Input Laguerre-Polynomial WASD Neuronet." In Toward Deep Neural Networks. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780429426445-3.

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Bania, Piotr, and Jerzy Baranowski. "Laguerre Polynomial Approximation of Fractional Order Linear Systems." In Lecture Notes in Electrical Engineering. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00933-9_15.

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Petković, M. S., L. Petković, and D. Živković. "Laguerre-like Methods for the Simultaneous Approximation of Polynomial Zeros." In Topics in Numerical Analysis. Springer Vienna, 2001. http://dx.doi.org/10.1007/978-3-7091-6217-0_15.

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Koranga, Bipin Singh, Sanjay Kumar Padaliya, and Vivek Kumar Nautiyal. "Laguerre Polynomials." In Special Functions and their Application. River Publishers, 2022. http://dx.doi.org/10.1201/9781003339595-6.

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Schweizer, Wolfgang. "Laguerre Polynomials." In Special Functions in Physics with MATLAB. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64232-7_17.

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Koelink, Erik, and Pablo Román. "Matrix Valued Laguerre Polynomials." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10850-2_16.

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Oldham, Keith B., Jan C. Myland, and Jerome Spanier. "The Laguerre Polynomials L n (x)." In An Atlas of Functions. Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-48807-3_24.

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Maqnus, Alphonse P. "Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials." In Orthogonal Polynomials and their Applications. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0083366.

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Cholewinski, Frank M. "13. A Class of Laguerre Type Polynomials." In Contemporary Mathematics. American Mathematical Society, 1988. http://dx.doi.org/10.1090/conm/075/13.

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Özarslan, Mehmet Ali, and Cemaliye Kürt. "Some Results on the Bivariate Laguerre Polynomials." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28443-9_9.

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Conference papers on the topic "Laguerre polynomial"

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Kozlova, E. S., A. A. Kovalev, A. A. Savelyeva, and V. V. Kotlyar. "Properties of Vortex Beams with a Squared Laguerre Polynomial." In 2024 Photonics & Electromagnetics Research Symposium (PIERS). IEEE, 2024. http://dx.doi.org/10.1109/piers62282.2024.10617975.

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Lee, Su-Ling, and Chien-Cheng Tseng. "GFT Centrality Computation Based on Laguerre Polynomial Graph Filtering Method." In 2024 IEEE 13th Global Conference on Consumer Electronics (GCCE). IEEE, 2024. https://doi.org/10.1109/gcce62371.2024.10760645.

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Pasha, Syed Ahmed, and Victor Solo. "A Nonlinear Hawkes Model Using Laguerre Orthogonal Polynomials." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10886716.

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Arceo, Alejandro, Rodrigo Gutierrez-Garza, Jorge de J. Lozoya-Santos, et al. "Compensators Design using Laguerre Polynomials Applied to a Real Steer-by-Wire System of Autonomous Vehicle." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10886253.

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Vladimirov, Alexey. "TMD PDFs in the Laguerre polynomial basis." In XXII. International Workshop on Deep-Inelastic Scattering and Related Subjects. Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.203.0034.

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Cheng-Yi Tian, Yan Shi, and Long Li. "Unconditionally stable Laguerre polynomial-based discontinuous Galerkin time-domain method." In 2016 IEEE International Conference on Computational Electromagnetics (ICCEM). IEEE, 2016. http://dx.doi.org/10.1109/compem.2016.7588627.

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Feng Liang, Hai Lin, and Gaofeng Wang. "Unconditionally stable PSTD method based on weighted Laguerre polynomial expansion." In 2009 International Conference on Microwave Technology and Computational Electromagnetics (ICMTCE 2009). IET, 2009. http://dx.doi.org/10.1049/cp.2009.1336.

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Perev, Kamen. "Laguerre polynomial approximation and model order reduction for linear systems." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4902454.

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Rego*, Eduarda C. G., Reynam C. Pestana, and Edvaldo Araujo. "Time-stepping evolution of wave equation using a Laguerre polynomial scheme." In SEG Technical Program Expanded Abstracts 2015. Society of Exploration Geophysicists, 2015. http://dx.doi.org/10.1190/segam2015-5879725.1.

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Struve, Demian, Andrés Lopez Pulzovan, and Thomas F. Geyer. "Assessment of a Laguerre Polynomial Based Sphere Decoding Algorithm for Direct MPC of Inverters." In 2024 European Control Conference (ECC). IEEE, 2024. http://dx.doi.org/10.23919/ecc64448.2024.10590812.

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