A survey on Christoffel–Darboux type identities of Legendre, Laguerre and Hermite polynomials

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• 作者：Asghar Arzhang
• 关键词：Christoffel–Darboux identity ; Cauchy kernel ; Legendre polynomials ; Laguerre polynomials ; Hermite polynomials ; 33D45 ; 33D50 ; 45E05
• 刊名：Mathematical Sciences
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：9
• 期：4
• 页码：193-197
• 全文大小：371 KB
• 参考文献：1.Arzhang, A.: A survey on Christoffel–Darboux-type identities of Chebyshev polynomials. Integral Transforms Spec. Funct. 24(10), 840-49 (2013). doi:10.-080/-0652469.-012.-62711 MATH MathSciNet CrossRef
  2.Andrews, G.E., Roy, R.: Special Functions. Cambridge University Press, Richard Askey, Cambridge (1999)MATH CrossRef
  3.Doha, E.H.: On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials. J. Phys. A 36, 5449-462 (2003)MATH MathSciNet CrossRef
  4.Karageorghis, A., Phillips, T.N.: On the coefficients of differentiated expansions of ultraspherical polynomials. Appl. Numer. Math. 9, 133-41 (1992)MATH MathSciNet CrossRef
  5.Poularikas, A.D.: The Transforms and Applications Handbook. CRC Press LLC, Boca Raton (2000)CrossRef
  6.Popov, B.S., Srivastava, H.M.: Linearization of a product of two polynomials of different orthogonal systems. Facta Univ. Ser. Math. Inform. 18, 1- (2003)MATH MathSciNet
  
• 作者单位：Asghar Arzhang (1)
  
  1. Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
  
• 刊物主题：Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：2251-7456

文摘

In this paper, we construct some new Christoffel–Darboux type identities for Legendre, Laguerre and Hermite polynomials. We obtain these types of identities for the derivatives of these polynomials. Keywords Christoffel–Darboux identity Cauchy kernel Legendre polynomials Laguerre polynomials Hermite polynomials