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Integral Transforms and Special Functions Volume 15, 2004 - Issue 1
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Original Articles

On the connection coefficients and recurrence relations arising from expansions in series of hermite polynomials

E. H. DohaCorrespondence[email protected]
Pages 13-29 | Published online: 13 May 2010

Citations (19)

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Read on this site (5)

W.M. Abd-Elhameed. (2015) New product and linearization formulae of Jacobi polynomials of certain parameters. Integral Transforms and Special Functions 26:8, pages 586-599.
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E. H. Doha, H. M. Ahmed & S. I. El-Soubhy. (2009) Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals. Integral Transforms and Special Functions 20:7, pages 491-503.
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Chun Shen & Meina Sun. (2008) On the neutral Hermite product of the distributions x ± and δ()(x). Integral Transforms and Special Functions 19:6, pages 387-398.
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E. H. Doha & H. M. Ahmed. (2006) Recurrence relation approach for expansion and connection coefficients in series of Hahn polynomials. Integral Transforms and Special Functions 17:11, pages 785-801.
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E. H. Doha & H. M. Ahmed. (2006) Recurrences and explicit formulae for the expansion and connection coefficients in series of classical discrete orthogonal polynomials. Integral Transforms and Special Functions 17:5, pages 329-353.
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Articles from other publishers (14)

E. H. Doha, Y. H. Youssri & M. A. Zaky. (2018) Spectral Solutions for Differential and Integral Equations with Varying Coefficients Using Classical Orthogonal Polynomials. Bulletin of the Iranian Mathematical Society 45:2, pages 527-555.
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W. M. Abd-Elhameed. (2017) New formulae between Jacobi polynomials and some fractional Jacobi functions generalizing some connection formulae. Analysis and Mathematical Physics 9:1, pages 73-98.
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E.H. Doha & Y.H. Youssri. (2019) On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain. Nonlinear Engineering 8:1, pages 318-327.
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E.H. Doha & W.M. Abd-Elhameed. (2016) New linearization formulae for the products of Chebyshev polynomials of third and fourth kinds. Rocky Mountain Journal of Mathematics 46:2.
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W. M. Abd-Elhameed, E. H. Doha & H. M. Ahmed. (2015) Linearization formulae for certain Jacobi polynomials. The Ramanujan Journal 39:1, pages 155-168.
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Eid H. DOHA, Waleed M. ABD-ELHAMEED & Mahmoud A. BASSUONY. (2015) On the coefficients of differentiated expansions and derivatives of chebyshev polynomials of the third and fourth kinds. Acta Mathematica Scientia 35:2, pages 326-338.
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M.R. Eslahchi, Mehdi Dehghan & S. Ahmadi_Asl. (2012) The general Jacobi matrix method for solving some nonlinear ordinary differential equations. Applied Mathematical Modelling 36:8, pages 3387-3398.
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E. H. Doha, A. H. Bhrawy & M. A. Saker. (2011) On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations. Boundary Value Problems 2011, pages 1-16.
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Eid H. Doha & Hany M. Ahmed. (2010) Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of quantum classical orthogonal polynomials. Journal of Advanced Research 1:3, pages 193-207.
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H.M. Ahmed & S.I. El-Soubhy. (2008) Recurrences and explicit formulae for the expansion and connection coefficients in series of ordinary Bessel polynomials. Applied Mathematics and Computation 199:2, pages 482-493.
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H. Chaggara & I. Lamiri. (2007) Linearization coefficients for Boas–Buck polynomial sets. Applied Mathematics and Computation 189:2, pages 1533-1549.
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E.H. Doha & H.M. Ahmed. (2006) On the coefficients of integrated expansions of Bessel polynomials. Journal of Computational and Applied Mathematics 187:1, pages 58-71.
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E H Doha & H M Ahmed. (2005) Efficient algorithms for construction of recurrence relations for the expansion and connection coefficients in series of Al-Salam–Carlitz I polynomials. Journal of Physics A: Mathematical and General 38:47, pages 10107-10121.
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E H Doha & H M Ahmed. (2004) Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials. Journal of Physics A: Mathematical and General 37:33, pages 8045-8063.
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