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Integral Transforms and Special Functions Volume 14, 2003 - Issue 1
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Original Articles

Explicit Formulae for the Coefficients of Integrated Expansions of Jacobi Polynomials and Their Integrals

E. H. Doha Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Pages 69-86 | Published online: 18 Oct 2010

Citations (18)

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Read on this site (1)

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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Articles from other publishers (17)

Hany M. Ahmed. (2021) Algorithms for Construction of Recurrence Relations for the Coefficients of the Fourier Series Expansions with Respect to Classical Discrete Orthogonal Polynomials. Bulletin of the Iranian Mathematical Society 48:3, pages 905-932.
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Richard Olu Awonusika & Afolabi Gabriel Ariwayo. (2022) Descriptions of fractional coefficients of Jacobi polynomial expansions. The Journal of Analysis.
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Richard Olu Awonusika. (2021) On Jacobi polynomials and fractional spectral functions on compact symmetric spaces. The Journal of Analysis 29:3, pages 987-1024.
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Richard Olu Awonusika. (2020) On Jacobi polynomials $${\mathscr {P}}_{k}^{(\alpha ,\beta )}$$ and coefficients $$c_{j}^{\ell }(\alpha ,\beta )$$ $$\left( k\ge 0, \ell =5,6; 1\le j\le \ell ; \alpha ,\beta > -1\right)$$. The Journal of Analysis 29:3, pages 649-667.
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José M. A. Matos, Maria João Rodrigues & João Carrilho de Matos. (2020) Explicit Formulae for Integro-Differential Operational Matrices. Mathematics in Computer Science 15:1, pages 45-61.
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E. H. Doha & W. M. Abd-Elhameed. (2014) Integrals of Chebyshev polynomials of third and fourth kinds: An application to solution of boundary value problems with polynomial coefficients. Journal of Contemporary Mathematical Analysis 49:6, pages 296-308.
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A.H. Bhrawy, M.M. Tharwat & A. Yildirim. (2013) A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations. Applied Mathematical Modelling 37:6, pages 4245-4252.
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E.H. Doha, W.M. Abd-Elhameed & Y.H. Youssri. (2012) Efficient spectral-Petrov–Galerkin methods for the integrated forms of third- and fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials. Applied Mathematics and Computation 218:15, pages 7727-7740.
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E.H. Doha, A.H. Bhrawy & M.A. Saker. (2011) Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations. Applied Mathematics Letters 24:4, pages 559-565.
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E. H. Doha, A. H. Bhrawy & R. M. Hafez. (2011) A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations. Abstract and Applied Analysis 2011, pages 1-21.
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A.H. Bhrawy & S.I. El-Soubhy. (2010) Jacobi spectral Galerkin method for the integrated forms of second-order differential equations. Applied Mathematics and Computation 217:6, pages 2684-2697.
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Eid H. Doha & Ali H. Bhrawy. (2009) A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations. Numerical Methods for Partial Differential Equations 25:3, pages 712-739.
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E.H. Doha & A.H. Bhrawy. (2008) Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials. Applied Numerical Mathematics 58:8, pages 1224-1244.
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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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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. (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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E H Doha. (2004) On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials. Journal of Physics A: Mathematical and General 37:3, pages 657-675.
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