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Volumn 37, Issue 2, 2014, Pages 383-398

On the coefficients of integrated expansions and integrals of chebyshev polynomials of third and fourth kinds

Author keywords

Boundary value problems; Chebyshev polynomials of third and fourth kinds; Expansion coefficients; Generalized hypergeometric functions

Indexed keywords


EID: 84897860705     PISSN: 01266705     EISSN: 21804206     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (43)

References (28)
  • 1
    • 33749531922 scopus 로고    scopus 로고
    • Solution of sixth order boundary value problems using non-polynomial spline technique
    • G. Akram and S. S. Siddiqi, Solution of sixth order boundary value problems using non-polynomial spline technique, Appl. Math. Comput. 181 (2006), no. 1, 708-720.
    • (2006) Appl. Math. Comput , vol.181 , Issue.1 , pp. 708-720
    • Akram, G.1    Siddiqi, S.S.2
  • 2
    • 85028115746 scopus 로고    scopus 로고
    • Matrix decomposition algorithms for elliptic boundary value problems: A survey
    • B. Bialecki, G. Fairweather and A. Karageorghis, Matrix decomposition algorithms for elliptic boundary value problems: A survey, Numer. Algorithms 56 (2011), no. 2, 253-295.
    • (2011) Numer. Algorithms , vol.56 , Issue.2 , pp. 253-295
    • Bialecki, B.1    Fairweather, G.2    Karageorghis, A.3
  • 4
  • 5
    • 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, Comput. Math. Appl. 21 (1991), no. 2-3, 115-122.
    • (1991) Comput. Math. Appl , vol.21 , Issue.2-3 , pp. 115-122
    • Doha, E.H.1
  • 6
    • 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), no. 2, 275-298.
    • (2002) J. Comput. Appl. Math , vol.139 , Issue.2 , pp. 275-298
    • Doha, E.H.1
  • 7
    • 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 35 (2002), no. 15, 3467-3478.
    • (2002) J. Phys. A , vol.35 , Issue.15 , pp. 3467-3478
    • Doha, E.H.1
  • 8
    • 0037303151 scopus 로고    scopus 로고
    • Explicit formulae for the coefficients of integrated expansions of Jacobi polynomials and their integrals
    • E. H. Doha, Explicit formulae for the coefficients of integrated expansions of Jacobi polynomials and their integrals, Integral Transforms Spec. Funct. 14 (2003), no. 1, 69-86.
    • (2003) Integral Transforms Spec. Funct , vol.14 , Issue.1 , pp. 69-86
    • Doha, E.H.1
  • 9
    • 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 36 (2003), no. 20, 5449-5462.
    • (2003) J. Phys. A , vol.36 , Issue.20 , pp. 5449-5462
    • Doha, E.H.1
  • 10
    • 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 (2004), no. 1, 13-29.
    • (2004) Integral Transforms Spec. Funct , vol.15 , Issue.1 , pp. 13-29
    • Doha, E.H.1
  • 11
    • 0037246330 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin algorithms for direct solution of secondorder equations using ultraspherical polynomials
    • electronic
    • E. H. Doha and W. M. Abd-Elhameed, Efficient spectral-Galerkin algorithms for direct solution of secondorder equations using ultraspherical polynomials, SIAM J. Sci. Comput. 24 (2002), no. 2, 548-571 (electronic).
    • (2002) SIAM J. Sci. Comput , vol.24 , Issue.2 , pp. 548-571
    • Doha, E.H.1    Abd-Elhameed, W.M.2
  • 12
    • 67649429772 scopus 로고    scopus 로고
    • Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of (2n + 1)th-order linear differential equations
    • E. H. Doha and W. M. Abd-Elhameed, Efficient spectral ultraspherical-dual-Petrov-Galerkin algorithms for the direct solution of (2n + 1)th-order linear differential equations, Math. Comput. Simulation 79 (2009), no. 11, 3221-3242.
    • (2009) Math. Comput. Simulation , vol.79 , Issue.11 , pp. 3221-3242
    • Doha, E.H.1    Abd-Elhameed, W.M.2
  • 13
    • 84858332341 scopus 로고    scopus 로고
    • Efficient spectral-Petrov-Galerkin methods for the integrated forms of thirdand fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials
    • E. H. Doha, W. M. Abd-Elhameed and Y. H. Youssri, Efficient spectral-Petrov-Galerkin methods for the integrated forms of thirdand fifth-order elliptic differential equations using general parameters generalized Jacobi polynomials, Appl. Math. Comput. 218 (2012), no. 15, 7727-7740.
    • (2012) Appl. Math. Comput , vol.218 , Issue.15 , pp. 7727-7740
    • Doha, E.H.1    Abd-Elhameed, W.M.2    Youssri, Y.H.3
  • 14
    • 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 37 (2004), no. 33, 8045-8063.
    • (2004) J. Phys. A , vol.37 , Issue.33 , pp. 8045-8063
    • Doha, E.H.1    Ahmed, H.M.2
  • 15
    • 66049087571 scopus 로고    scopus 로고
    • A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations
    • E. H. Doha and A. H. Bhrawy, A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations, Numer. Methods Partial Differential Equations 25 (2009), no. 3, 712-739.
    • (2009) Numer. Methods Partial Differential Equations , vol.25 , Issue.3 , pp. 712-739
    • Doha, E.H.1    Bhrawy, A.H.2
  • 16
    • 79955463402 scopus 로고    scopus 로고
    • Application of Taylor series in obtaining the orthogonal operational matrix
    • M. R. Eslahchi and M. Dehghan, Application of Taylor series in obtaining the orthogonal operational matrix, Comput. Math. Appl. 61 (2011), no. 9, 2596-2604.
    • (2011) Comput. Math. Appl , vol.61 , Issue.9 , pp. 2596-2604
    • Eslahchi, M.R.1    Dehghan, M.2
  • 17
    • 84859834645 scopus 로고    scopus 로고
    • The general Jacobi matrix method for solving some nonlinear ordinary differential equations
    • M. R. Eslahchi, M. Dehghan and S. Ahmadi-Asl, The general Jacobi matrix method for solving some nonlinear ordinary differential equations, Appl. Math. Model 36 (2012), 3387-3398.
    • (2012) Appl. Math. Model , vol.36 , pp. 3387-3398
    • Eslahchi, M.R.1    Dehghan, M.2    Ahmadi-Asl, S.3
  • 18
    • 84856213629 scopus 로고    scopus 로고
    • The third and fourth kinds of Chebyshev polynomials and best uniform approximation
    • M. R. Eslahchi, M. Dehghan and S. Amani, The third and fourth kinds of Chebyshev polynomials and best uniform approximation, Math. Comput. Modelling 55 (2012), no. 5-6, 1746-1762.
    • (2012) Math. Comput. Modelling , vol.55 , Issue.5-6 , pp. 1746-1762
    • Eslahchi, M.R.1    Dehghan, M.2    Amani, S.3
  • 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), no. 1, 129-132.
    • (1988) J. Comput. Appl. Math , vol.21 , Issue.1 , pp. 129-132
    • Karageorghis, A.1
  • 22
    • 0008089454 scopus 로고
    • On the coefficients of differentiated expansions of ultraspherical polynomials
    • A. Karageorghis and T. N. Phillips, On the coefficients of differentiated expansions of ultraspherical polynomials, Appl. Numer. Math. 9 (1992), no. 2, 133-141.
    • (1992) Appl. Numer. Math , vol.9 , Issue.2 , pp. 133-141
    • Karageorghis, A.1    Phillips, T.N.2
  • 23
    • 54049090479 scopus 로고    scopus 로고
    • Spline collocation method for solving linear sixthorder boundary-value problems
    • A. Lamnii, H. Mraoui, D. Sbibih, A. Tijini and A. Zidna, Spline collocation method for solving linear sixthorder boundary-value problems, Int. J. Comput. Math. 85 (2008), no. 11, 1673-1684.
    • (2008) Int. J. Comput. Math , vol.85 , Issue.11 , pp. 1673-1684
    • Lamnii, A.1    Mraoui, H.2    Sbibih, D.3    Tijini, A.4    Zidna, A.5
  • 24
    • 0009031763 scopus 로고
    • Chebyshev polynomial approximations for the L-membrane eigenvalue problem
    • J. C. Mason, Chebyshev polynomial approximations for the L-membrane eigenvalue problem, SIAM J. Appl. Math. 15 (1967), 172-186.
    • (1967) SIAM J. Appl. Math , vol.15 , pp. 172-186
    • Mason, J.C.1
  • 25
    • 0027842087 scopus 로고
    • Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms
    • J. C. Mason, Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms, J. Comput. Appl. Math. 49 (1993), no. 1-3, 169-178.
    • (1993) J. Comput. Appl. Math , vol.49 , Issue.1-3 , pp. 169-178
    • Mason, J.C.1
  • 27
    • 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), no. 4, 455-459.
    • (1988) IMA J. Numer. Anal , vol.8 , Issue.4 , pp. 455-459
    • Phillips, T.N.1
  • 28
    • 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), no. 3, 823-830.
    • (1990) SIAM J. Numer. Anal , vol.27 , Issue.3 , pp. 823-830
    • Phillips, T.N.1    Karageorghis, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.