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Application of Eigenkets of Bosonic Creation Operator in Deriving Some New Formulas of Associated Laguerre Polynomials 被引量:1
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作者 FAN Hong-Yi WANG Tong-Tong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第8期315-320,共6页
Using the resolution of unity composed of bosonic creation operator's eigenkets and annihilation operator's un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we de... Using the resolution of unity composed of bosonic creation operator's eigenkets and annihilation operator's un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L^ρm (|z|^2) and its generalized generating function formula. A series of recursive relations regarding to L^ρm (|z|^2) are also deduced in the context of the Fock representation by algebraic method. 展开更多
关键词 bosonic creation operator laguerre polynomials contour integration
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CERTAIN ASYMPTOTIC EXPANSIONS FOR LAGUERRE POLYNOMIALS AND CHARLIER POLYNOMIALS
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作者 L. C. Hsu 《Analysis in Theory and Applications》 1995年第1期94-104,共11页
Here proposed are certain asymptotic expansion formulas for Ln(w-1)(λz) and Cn(ω)(λz) in whichO(λ) and n = 0(λ1/2 )(λ→∞) , z being x complex number. Also presented are certain estimates for the remainders(erro... Here proposed are certain asymptotic expansion formulas for Ln(w-1)(λz) and Cn(ω)(λz) in whichO(λ) and n = 0(λ1/2 )(λ→∞) , z being x complex number. Also presented are certain estimates for the remainders(error bounds) of the asymptotic expansions within the regions D1( - ∞<Rez≤1/2 (ω/λ) and D2(1/2 (ω/λ)≤Re.'C00)? respectively. 展开更多
关键词 CERTAIN ASYMPTOTIC EXPANSIONS FOR laguerre polynomials AND CHARLIER polynomials
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Some New Generating Functions for the Modified Laguerre Polynomials
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作者 Nejla Ozmen 《Advances in Applied Mathematics and Mechanics》 SCIE 2019年第6期1398-1414,共17页
In this paper,we obtain some new results on bilateral generating functions of the modified Laguerre polynomials.We also get generating function relations between the modified Laguerre polynomials and the generalized L... In this paper,we obtain some new results on bilateral generating functions of the modified Laguerre polynomials.We also get generating function relations between the modified Laguerre polynomials and the generalized Lauricella functions.Some special cases and important applications are also discussed. 展开更多
关键词 Modified laguerre polynomials generating function multilinear and multilateral generating function recurrence relations generalized Lauricella function
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Solution of time-domain Maxwell equation with PML by using modified Laguerre polynomials
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作者 LI LianLin LI Fang 《Science in China(Series F)》 2008年第5期550-559,共10页
In this work, a stable numerical algorithm proposed by Chung et al. for the time-domain Maxwell equations is generalized. The time-domain Maxwell equations are solved by expressing the transient behaviors in terms of ... In this work, a stable numerical algorithm proposed by Chung et al. for the time-domain Maxwell equations is generalized. The time-domain Maxwell equations are solved by expressing the transient behaviors in terms of the modified Laguerre polynomials, and then the original equations of the initial value and boundary value can be transformed into a series of problems independent of the time variable. In this case the method of finite difference (FD), the finite element method (FEM), the method of moment (MoM), etc. or the combination of these methods can be used to solve the problems. Finally, a numerical model is provided for the scattering problem with perfect matched layer (PML) by using FD. The comparison between the results of the proposed method and FDTD is presented to verify the proposed new method. 展开更多
关键词 time-domain Maxwell equations modified laguerre polynomials boundary value problems
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Coherent state and normal ordering method for transiting Hermite polynomials to Laguerre polynomials 被引量:3
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作者 FAN HongYi ZHOU Jun 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2012年第4期605-608,共4页
By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials. We also derive the new reciprocal relation of Laguerre... By virtue of the coherent state representation and the operator ordering method we find a new approach for transiting Hermite polynomials to Laguerre polynomials. We also derive the new reciprocal relation of Laguerre polynomials ∑n=0 (-1)n (n^l)Ln (x) = x^l/n, n-O and its application in deriving the sum rule of the Wingner function of Fock states is demonstrated. Some new expansion identities about the operator Laguerre polynomial are also derived. This opens a new route of deriving mathematical polynomials formulas by virtute of the quantum mechanical representations and operator ordering technique. 展开更多
关键词 coherent state Hermite polynomial laguerre polynomial normal ordering
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Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials 被引量:1
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作者 Alfred Wunsche 《Applied Mathematics》 2015年第12期2142-2168,共27页
The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polyn... The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions. 展开更多
关键词 laguerre and Hermite polynomials laguerre 2D polynomials Jacobi polynomials Mehler Formula SU(1 1)Operator Disentanglement Gaussian Convolutions
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A NOTE ON SOBOLEV ORTHOGONALITY FOR LAGUERRE MATRIX POLYNOMIALS
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作者 Zhihui Zhu Zhongkai Li 《Analysis in Theory and Applications》 2007年第1期26-34,共9页
Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×... Abstract. Let {L(Ln^(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0,∞) byLn^(A,λ)(x)=n!/(-λ)^n ∑nk-0(-λ)^k/k!(n-k)!(A+I)n[(A+I)k]^-1x^k,where A ∈ C^r×r. It is known that {Ln^(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) 〉 -1 for every z E or(a). In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln^(A,λ)(x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case. 展开更多
关键词 laguerre matrix polynomial Sobolev orthogonality matrix moment functional
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Evaluation of Certain Integrals Involving the Product of Classical Hermite's Polynomials Using Laplace Transform Technique and Hypergeometric Approach
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作者 M.I.Qureshi Saima Jabee 《Analysis in Theory and Applications》 CSCD 2017年第4期355-365,共11页
In this paper some novel integrals associated with the product of classical Hermite's polynomials ∫-∞+∞(x2)mexp(-x2){Hr(x)}2dx,∫0∞exp(-x2)H2k(x)H2s+1(x)dx,∫0∞exp(-x2)H2k(x)H2s(x)dx and ∫0... In this paper some novel integrals associated with the product of classical Hermite's polynomials ∫-∞+∞(x2)mexp(-x2){Hr(x)}2dx,∫0∞exp(-x2)H2k(x)H2s+1(x)dx,∫0∞exp(-x2)H2k(x)H2s(x)dx and ∫0∞exp(-x2)H2k+1(x)H2s+1(x)dx, are evaluated using hypergeometric approach and Laplace transform method, which is a different approach from the approaches given by the other authors in the field of spe- cial functions. Also the results may be of significant nature, and may yield numerous other interesting integrals involving the product of classical Hermite's polynomials by suitable simplifications of arbitrary parameters. 展开更多
关键词 Gauss's summation theorem classical Hermite's polynomials generalized hyperge-ometric function generalized laguerre's polynomials.
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A new quantum mechanical photon counting distribution formula
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作者 袁洪春 范洪义 胡利云 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第11期5-8,共4页
By virtue of the density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we calculate photon counting dis... By virtue of the density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we calculate photon counting distributions for some given light fields. It is found that the pure squeezed state's photon counting distribution is related to the Legendre function, which is a new result. 展开更多
关键词 P-representation photon counting distribution laguerre polynomial Legendre polynomial
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Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems 被引量:1
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作者 F.Auteri L.Quartapelle 《Communications in Computational Physics》 SCIE 2012年第10期1329-1358,共30页
In this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory.An original Petrov-Galerkin formulation of ... In this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory.An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown.A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows.The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation.The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms. 展开更多
关键词 laguerre polynomials semi-infinite interval boundary layer theory Falkner-Skan equation Cooke equation Orr-Sommerfeld equation linear stability of parallel flows
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Self-Reciprocal Polynomials of Binomial Type
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作者 Qin FANG Tian Ming WANG 《Journal of Mathematical Research and Exposition》 CSCD 2010年第4期628-636,共9页
In this paper, we define the self-inverse sequences related to sequences of polynomials of binomial type, and give some interesting results of these sequences. Moreover, we study the self-inverse sequences related to ... In this paper, we define the self-inverse sequences related to sequences of polynomials of binomial type, and give some interesting results of these sequences. Moreover, we study the self-inverse sequences related to the Laguerre polynomials. 展开更多
关键词 self-inverse sequences sequences of binomial type basic sequences laguerre polynomials.
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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian
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作者 Jiaqi Zhang Yin Yang Zhaojie Zhou 《Advances in Applied Mathematics and Mechanics》 SCIE 2023年第6期1631-1654,共24页
In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated.To deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre ... In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated.To deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is utilized.The first order optimality condition of the extended optimal control problem is derived.A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed.A priori error estimates for the spectral Galerkin discrete scheme is proved.Numerical experiments are presented to show the effectiveness of our methods and to verify the theoretical findings. 展开更多
关键词 Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted laguerre polynomials
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Solutions of the Schrdinger Equation with Quantum Mechanical Gravitational Potential Plus Harmonic Oscillator Potential 被引量:1
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作者 B.I.Ita A.I.Ikeuba A.N.Ikot 《Communications in Theoretical Physics》 SCIE CAS CSCD 2014年第2期149-152,共4页
The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eig... The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained. 展开更多
关键词 Schrodinger equation quantum mechanical gravitational potential harmonic oscillator Nikiforov-Uvarov method laguerre polynomials
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Some Representations of Unified Voigt Functions
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作者 M.KAMARUJJAMA DineshSINGH 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期865-868,共4页
The authors derive a set of unified representations of the Voigt functions in terms of familiar special functions of Mathematical Physics. Some deductions from these representations are also considered.
关键词 Voigt functions Bessel functions Confluent hypergeometric function laguerre and Hermite polynomials
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