关于拉盖尔多项式的一些新的恒等式

doi:10.6040/j.issn.1671-9352.0.2019.207

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (4): 85-91.doi: 10.6040/j.issn.1671-9352.0.2019.207

• • 上一篇

关于拉盖尔多项式的一些新的恒等式

张佳凡,吕星星^*

西北大学数学学院, 陕西西安 710100

发布日期:2020-04-09
作者简介:张佳凡(1995— ), 女, 硕士研究生, 研究方向为数论. E-mail:zhangjiafan@stumail.nwu.edu.cn*通信作者简介:吕星星(1993— ), 女, 博士研究生, 研究方向为数论. E-mail:lvxingxing@stumail.nwu.edu.cn
基金资助:
国家自然科学基金资助项目(11771351,11826205)

Some new identities on Laguerre polynomials

ZHANG Jia-fan, LYU Xing-xing^*

School of Mathematics, Northwest University, Xian 710100, Shaanxi, China

Published:2020-04-09

摘要/Abstract

摘要： 利用初等和组合的方法研究了拉盖尔多项式的基本性质, 并给出了一些新的恒等式。

关键词: 拉盖尔多项式, 初等和组合方法, 递归多项式, 恒等式

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

中图分类号:

O156.4

张佳凡,吕星星. 关于拉盖尔多项式的一些新的恒等式[J]. 《山东大学学报(理学版)》, 2020, 55(4): 85-91.

ZHANG Jia-fan, LYU Xing-xing. Some new identities on Laguerre polynomials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(4): 85-91.

[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+u_n(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.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

关于拉盖尔多项式的一些新的恒等式

Some new identities on Laguerre polynomials

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 6

多维度评价

本文评价

推荐阅读 0

[1]	王啸. 关于特征和与指数和混合均值的一个注记[J]. 《山东大学学报(理学版)》, 2019, 54(12): 97-101.
[2]	宋贤梅,熊蕾. Z_2^a+uZ_2^a 上线性码的MacWilliams恒等式及自对偶码[J]. 山东大学学报（理学版）, 2016, 51(2): 72-78.
[3]	邓利华, 邓玉平, Louis W. Shapiro. 对称格路与恒等式[J]. 山东大学学报（理学版）, 2015, 50(04): 82-89.
[4]	刘修生,刘花璐. 环Fp+vFp上线性码的MacWilliams恒等式[J]. J4, 2013, 48(12): 61-65.
[5]	吴校贵，张建华. 全矩阵代数上保Jacobi恒等式的线性映射[J]. J4, 2009, 44(1): 49-52 .
[6]	李志荣,李映辉 . 一类新的包含Genocchi数与Riemann Zeta函数求和的计算公式[J]. J4, 2007, 42(4): 79-83 .