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Volumn 20, Issue 7, 2009, Pages 491-503

Explicit formulae for the coefficients of integrated expansions of Laguerre and Hermite polynomials and their integrals

Author keywords

Expansion coefficients; Laguerre and Hermite polynomials; Spectral methods

Indexed keywords


EID: 70449394642     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652460802030672     Document Type: Article
Times cited : (16)

References (29)
  • 4
    • 0030375661 scopus 로고    scopus 로고
    • An efficient spectral methods for ordinary differential equations with rational function coefficients
    • E.A. Coutsias, T. Hagstorm, and D. Torres, An efficient spectral methods for ordinary differential equations with rational function coefficients, Math. Comput. 65 (1996), pp. 611-635.
    • (1996) Math. Comput. , vol.65 , pp. 611-635
    • Coutsias, E.A.1    Hagstorm, T.2    Torres, D.3
  • 5
    • 0025226701 scopus 로고
    • An accurate solution of parabolic equations by expansion in ultraspherical polynomials
    • E.H. Doha, An accurate solution of parabolic equations by expansion in ultraspherical polynomials, J. Comput. Math. Appl. 19 (1990), pp. 75-88.
    • (1990) J. Comput. Math. Appl. , vol.19 , pp. 75-88
    • Doha, E.H.1
  • 6
    • 0000581486 scopus 로고
    • The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
    • E.H. Doha, The coefficients of differentiated expansions and derivatives of ultraspherical polynomials, J. Comput. Math. Appl. 21 (1991), pp. 115-122.
    • (1991) J. Comput. Math. Appl. , vol.21 , pp. 115-122
    • Doha, E.H.1
  • 7
    • 0012680079 scopus 로고    scopus 로고
    • The coefficients of differentiated expansions of double and triple ultraspherical polynomials
    • E.H. Doha, The coefficients of differentiated expansions of double and triple ultraspherical polynomials, Ann. Univ. Sci. Budapest, Sect. Comput. 19 (2000), pp. 57-73.
    • (2000) Ann. Univ. Sci. Budapest, Sect. Comput. , vol.19 , pp. 57-73
    • Doha, E.H.1
  • 8
    • 0037134397 scopus 로고    scopus 로고
    • On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
    • E.H. Doha, On the coefficients of differentiated expansions and derivatives of Jacobi polynomials, J. Phys. A: Math. Gen. 35 (2002), pp. 3467-3478.
    • (2002) J. Phys. A: Math. Gen. , vol.35 , pp. 3467-3478
    • Doha, E.H.1
  • 9
    • 0037082968 scopus 로고    scopus 로고
    • On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
    • E.H. Doha, On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations, J. Comput. Appl. Math. 139 (2002), pp. 275-298.
    • (2002) J. Comput. Appl. Math. , vol.139 , pp. 275-298
    • Doha, E.H.1
  • 10
    • 0037303151 scopus 로고    scopus 로고
    • Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals
    • E.H. Doha, Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals, Integral Transforms Spec. Funct. 14(1) (2003), pp. 69-86.
    • (2003) Integral Transforms Spec. Funct. , vol.14 , Issue.1 , pp. 69-86
    • Doha, E.H.1
  • 11
    • 0038176549 scopus 로고    scopus 로고
    • On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials
    • E.H. Doha, On the connection coefficients and recurrence relations arising from expansions in series of Laguerre polynomials, J. Phys. A: Math. Gen. 36 (2003), pp. 5449-5462.
    • (2003) J. Phys. A: Math. Gen. , vol.36 , pp. 5449-5462
    • Doha, E.H.1
  • 12
    • 0842325088 scopus 로고    scopus 로고
    • On the connection coefficients and recurrence relations arising from expansions in series of Hermite polynomials
    • E.H. Doha, On the connection coefficients and recurrence relations arising from expansions in series of Hermite polynomials, Integral Transforms Spec. Funct. 15 (1) (2004), pp. 13-29.
    • (2004) Integral Transforms Spec. Funct. , vol.15 , Issue.1 , pp. 13-29
    • Doha, E.H.1
  • 13
    • 0742271179 scopus 로고    scopus 로고
    • On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials
    • E.H. Doha, On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials, J. Phys. A: Math. Gen. 37 (2004), pp. 657-675.
    • (2004) J. Phys. A: Math. Gen. , vol.37 , pp. 657-675
    • Doha, E.H.1
  • 14
    • 0037246330 scopus 로고    scopus 로고
    • Efficient spectral Galerkin-algorithms for direct solution of second-order equations using ultraspherical polynomials
    • E.H. Doha and W.M. Abd-Elhameed, Efficient spectral Galerkin-algorithms for direct solution of second-order equations using ultraspherical polynomials, SIAM J. Sci. Comput. 24 (2002), pp. 548-571.
    • (2002) SIAM J. Sci. Comput. , vol.24 , pp. 548-571
    • Doha, E.H.1    Abd-Elhameed, W.M.2
  • 15
    • 4344713401 scopus 로고    scopus 로고
    • Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials
    • E.H. Doha and H.M. Ahmed, Recurrences and explicit formulae for the expansion and connection coefficients in series of Bessel polynomials, J. Phys. A: Math. Gen. 37 (2004), pp. 8045-8063.
    • (2004) J. Phys. A: Math. Gen. , vol.37 , pp. 8045-8063
    • Doha, E.H.1    Ahmed, H.M.2
  • 16
    • 0012724290 scopus 로고    scopus 로고
    • An efficient double Legendre spectral method for parabolic and elliptic partial differential equations
    • E.H. Doha and F.M.R. Al-Kholi, An efficient double Legendre spectral method for parabolic and elliptic partial differential equations, Int. J. Comput. Math., 78 (2001), pp. 413-432.
    • (2001) Int. J. Comput. Math. , vol.78 , pp. 413-432
    • Doha, E.H.1    Al-Kholi, F.M.R.2
  • 17
    • 0003153174 scopus 로고    scopus 로고
    • An accurate double Chebyshev spectral approximation for parabolic partial differential equations
    • E.H. Doha and M.A. Helal, An accurate double Chebyshev spectral approximation for parabolic partial differential equations, J. Egypt. Math. Sco. 5 (1997), pp. 83-101.
    • (1997) J. Egypt. Math. Sco. , vol.5 , pp. 83-101
    • Doha, E.H.1    Helal, M.A.2
  • 18
    • 33845416649 scopus 로고
    • Numerical analysis of spectral methods: Theory and applications
    • Society of Industrial and Applied Mathematics, Philadelphia, PA
    • D. Gottlieb and S.A. Orszag, Numerical analysis of spectral methods: theory and applications, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 26, Society of Industrial and Applied Mathematics, Philadelphia, PA, 1977.
    • (1977) CBMS-NSF Regional Conference Series in Applied Mathematics , vol.26
    • Gottlieb, D.1    Orszag, S.A.2
  • 19
    • 49249143705 scopus 로고
    • The accurate solution of Poisson's equation by Chebyshev polynomials
    • D.B. Haidvogel and T. Zang, The accurate solution of Poisson's equation by Chebyshev polynomials, J. Comput. Phys. 30 (1979), pp. 167-180.
    • (1979) J. Comput. Phys. , vol.30 , pp. 167-180
    • Haidvogel, D.B.1    Zang, T.2
  • 20
    • 0035123550 scopus 로고    scopus 로고
    • A Chebyshev spectral method for solving Korteweg-deVries equation with hydrodynamical application
    • M.A. Helal, A Chebyshev spectral method for solving Korteweg-deVries equation with hydrodynamical application, Chaos Solitons and Fractals 12 (2001), pp. 943-950.
    • (2001) Chaos Solitons and Fractals , vol.12 , pp. 943-950
    • Helal, M.A.1
  • 21
    • 0000036756 scopus 로고
    • A note on the Chebyshev coefficients of the general-order derivative of an infinitely differentiable function
    • A. Karageorghis, A note on the Chebyshev coefficients of the general-order derivative of an infinitely differentiable function, J. Comput. Appl. Math. 21 (1988), pp. 129-132.
    • (1988) J. Comput. Appl. Math. , vol.21 , pp. 129-132
    • Karageorghis, A.1
  • 22
    • 0008089454 scopus 로고
    • On the coefficients of differentiated expansions of ultraspherical polynomials
    • ICASE Report No. 89-65, NASA Langley Research Center, Hampton, VA, 1989 and
    • A. Karageorghis and T.N. Phillips, On the coefficients of differentiated expansions of ultraspherical polynomials, ICASE Report No. 89-65, NASA Langley Research Center, Hampton, VA, 1989 and Appl. Num. Math. 9 (1992), pp. 133-141.
    • (1992) Appl. Num. Math. , vol.9 , pp. 133-141
    • Karageorghis, A.1    Phillips, T.N.2
  • 24
    • 0001324079 scopus 로고
    • On the Legendre coefficients of a general-order derivative of an infinitely differentiable function
    • T.N. Phillips, On the Legendre coefficients of a general-order derivative of an infinitely differentiable function, IMA. J. Numer. Anal. 8 (1988), pp. 455-459.
    • (1988) IMA. J. Numer. Anal. , vol.8 , pp. 455-459
    • Phillips, T.N.1
  • 25
    • 0025448724 scopus 로고
    • On the coefficients of integrated expansions of ultraspherical polynomials
    • T.N. Phillips and A. Karageorghis, On the coefficients of integrated expansions of ultraspherical polynomials, SIAM J. Numer. Anal. 27 (1990), pp. 823-830.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 823-830
    • Phillips, T.N.1    Karageorghis, A.2
  • 27
    • 0032498758 scopus 로고    scopus 로고
    • Expansions in series of orthogonal polynomials
    • J. Sánchez-Ruiz and J.S. Dehesa, Expansions in series of orthogonal polynomials, J. Comput.Appl. Math. 89 (1998), pp. 155-170.
    • (1998) J. Comput.Appl. Math. , vol.89 , pp. 155-170
    • Sánchez-Ruiz, J.1    Dehesa, J.S.2
  • 28
    • 0031556715 scopus 로고    scopus 로고
    • An accurate solution of Poisson equation by the Chebyshev-Tau methods
    • H.I. Siyyam and M.I. Syam, An accurate solution of Poisson equation by the Chebyshev-Tau methods, J. Comput. Appl. Math. 85 (1997), pp. 1-10.
    • (1997) J. Comput. Appl. Math. , vol.85 , pp. 1-10
    • Siyyam, H.I.1    Syam, M.I.2


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