JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 85-91.doi: 10.6040/j.issn.1671-9352.0.2019.207

Previous Articles    

Some new identities on Laguerre polynomials

ZHANG Jia-fan, LYU Xing-xing*   

  1. School of Mathematics, Northwest University, Xian 710100, Shaanxi, China
  • Published:2020-04-09

PDF (PC)

614

Abstract: This paper uses the methods of elementary and combination to study the basic properties of Laguerre polynomials, and gives some new identities for Laguerre polynomials.

Key words: Laguerre polynomial, elementary and combinatorial method, recursive polynomial, identity

CLC Number: 

  • O156.4
[1] CHIHARA T S. An introduction to orthogonal polynomials, Gordon and breach[M]. New York: [s.n.] , 1978.
[2] CHATTERJEA S K. On a generating function of Languerre polynomials[J]. Bollettino dell'Unione Matematica Italiana,1962, 17:179-182.
[3] KOEKOEK R, SWARTTOUW R F. The askey-scheme of hypergeometric orthogonal polynomials and its q-analogue[R] // Report 98-17. Delft: Delft University of Technology, 1998.
[4] SZEGÓ G. Orthogonal polynomials[M] //American Mathematical Society Colloquim Publication Series, Vol 23. Providence, RI: American Mathematical Society, 1975.
[5] GOMEZ-ULLATE D, GRANDATI Y, MILSON R. Shape invariance and equivalence relations for pseudo-Wronskians of Laguerre and Jacobi polynomials[J]. Journal of Physics A-Mathematical and Theoretical, 2018, 51:345201.
[6] KIM T, KIM D, DOLGY V. Sums of finite products of Legendre and Laguerre polynomials[J]. Advances in Difference Equation, 2018, 277. DOI:10.1186/s13662-018-1740-6.
[7] HUANG Li, ZHANG Haoxuan, LIAO Yi. Discontinuous Galerkin method using Laguerre polynomials for solving a time-domain electric field integral equation[J]. IEEE Antennas and Wireless Propagation Letters, 2018, 17:865-868.
[8] YE Wei, ZHANG Kuizheng, ZHANG Haoliang. Laguerre-polynomial-weighted squeezed vacuum: generation and its properties of entanglement[J]. Laser Physics Letters, 2018, 15:025204.
[9] ALOUI B. Characterization of Laguerre polynomials as orthogonal polynomials connected by the Laguerre degree raising shift operator[J]. Ramanujan Journal, 2018, 45:475-481.
[10] JINDAL A, LAISHRAM S, SARMA R. Irreducibility and Galois groups of generalized Laguerre polynomials[J]. Journal of Number Theory, 2018, 183:388-406.
[11] OKSUZER O, KARSLI H, YESILDAL F. Rate of convergence of the Bezier variant of an operator involving Laguerre polynomials[J]. Mathematical Methods in Applied Sciences, 2018, 41:912-919.
[12] SARANYA N G, SHOREY T N. Irreducibility of generalized Laguerre polynomials L1/2+un(x2) with -18≤u≤-2[J]. Acta Arithmetica, 2018, 184:363-383.
[13] GHAYASUDDIN M, KHAN N, KHAN S W. Some finite integrals involving the product of Bessel function with Jacobi and Laguerre polynomials[J]. Communications of the KMS, 2018, 33:1013-1024.
[14] YUAN Jiawei, JIANG Yaolin. A parameterised model order reduction method for parametric systems based on Laguerre polynomials[J]. International Journal of Control, 2018, 91:1861-1872.
[15] SHARAPUDINOV I I, MAGOMED-KASUMOV M G. On representation of a solution to the Cauchy problem by a Fourier series in Sobolev-orthogonal polynomials generated by Laguerre polynomials[J]. Differential Equations, 2018, 54:49-66.
[16] NIU Dawei, LI Long. q-Laguerre polynomials and related q-partial differential equations[J]. Journal of Difference Equations and Applications, 2018, 24:375-390.
[17] YE Wei, ZHOU Weidong, ZHANG Haoliang. Laguerre polynomial excited coherent state: generation and nonclassical properties[J]. Laser Physics Letters, 2017, 14:115201.
[18] KHAN S, KHAN R. Modified relativistic Laguerre polynomials. Monomiality and Lie algebraic methods[J]. Georgian Mathematical Journal, 2016, 23:381-386.
[19] HAN Pengju, CHEN Yang. The recurrence coeffcients of a semi-classical Laguerre polynomials and the large n asymptotics of the associated Hankel determinant[J]. Random Matrices-Theory and Applications, 2017, 6:1740002.
[20] DESHWAL S, ACU A M, AGRAWAL P N. Pointwise approximation by Bézier variant of an operator based on Laguerre polynomials[J]. Journal of Mathematical Inequalities, 2018, 12:693-707.
[21] APOSTOL T M. Introduction to analytic number theory[M]. New York: Springer-Verlag, 1976.
[1] WANG Xiao. A note on the hybrid power mean of the character sums and exponential sums [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 97-101.
[2] LUO Peng, YANG Xiao-yuan. Identity-based encryption in multiple PKG environment based on ring signature [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(6): 64-68.
[3] WANG Wei-li, HU Bin, ZHAO Xiu-feng. An efficient multi-identity-based fully homomorphic encryption scheme [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(5): 85-94.
[4] QU Juan, LI Yan-ping. A secure dynamic identity-based remote user authentication scheme [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 37-42.
[5] ZHU Zhi-qiang, MA Ke-xin, SUN Lei. A zero-knowledge proof based remote desktop authentication protocol [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(9): 47-52.
[6] . A system of monitoring and protecting Android privacy leakage [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(9): 59-67.
[7] SONG Xian-mei, XIONG Lei. MacWilliams identity and self-dual codes of linear codes over Z2a+uZ2a [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 72-78.
[8] YUAN Bian-qing, LIU Ji-qiang. An offline sharable mCoupons scheme based on NFC [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(09): 56-61.
[9] LIU Xiu-sheng, LIU Hua-lu. MacWilliams identities of the linear codes over ring Fp+vFp [J]. J4, 2013, 48(12): 61-65.
[10] . Scheme of hierarchical content extraction signature based on non-credible PKG identity-based signature [J]. J4, 2012, 47(9): 7-14.
[11] WANG Juan1,2, HE Qi1, YAN Fei1,2, JIANG Wan-wei1, YANG Ming1, WANG Yan1. A user-centric identity management and authentication system for mobile Internet [J]. J4, 2012, 47(11): 12-17.
[12] LIANG Shao-Hui, DIAO Ban. Resarches on some properties of a strong FS-Poset [J]. J4, 2009, 44(8): 51-55.
[13] WU Xiaogui, ZHANG Jianhua. Linear maps preserving Jacobi identity on the full matrix algebras [J]. J4, 2009, 44(1): 49-52 .
[14] LI Zhi-rong and LI Ying-hui . A new kind of summation formulae involving the Genocchi number and Riemann Zeta function [J]. J4, 2007, 42(4): 79-83 .
[15] LIU Xiao-dong,JIANG Ya-li,LI Da-xing . Two biometric identities based signature schemes [J]. J4, 2007, 42(12): 24-28 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd