메뉴 건너뛰기




Volumn 15, Issue 1, 2004, Pages 13-29

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

Author keywords

Connection coefficients; Hermite expansion coefficients; Hermite polynomials; Jacobi and Laguerre polynomials; Recurrence relations

Indexed keywords


EID: 0842325088     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652460310001600618     Document Type: Article
Times cited : (22)

References (24)
  • 3
    • 0000581486 scopus 로고
    • The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
    • Doha, E. H. (1991). The coefficients of differentiated expansions and derivatives of ultraspherical polynomials. J. Comput. Math. Appl., 21, 115-122.
    • (1991) J. Comput. Math. Appl. , vol.21 , pp. 115-122
    • Doha, E.H.1
  • 4
    • 0041185610 scopus 로고
    • The first and second kinds Chebyshev coefficients of the moments of the general-order derivative of an infinitely differentiable function
    • Doha, E. H. (1994). The first and second kinds Chebyshev coefficients of the moments of the general-order derivative of an infinitely differentiable function. Internat. J. Comput. Math., 51, 21-35.
    • (1994) Internat. J. Comput. Math. , vol.51 , pp. 21-35
    • Doha, E.H.1
  • 5
    • 0032498763 scopus 로고    scopus 로고
    • The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
    • Doha, E. H. (1998). The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function. J. Comput. Appl. Math., 89, 53-72.
    • (1998) J. Comput. Appl. Math. , vol.89 , pp. 53-72
    • Doha, E.H.1
  • 6
    • 0037134397 scopus 로고    scopus 로고
    • On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
    • Doha, E. H. (2002). On the coefficients of differentiated expansions and derivatives of Jacobi polynomials. J. Phys. A: Math. Gen., 35, 3467-3478.
    • (2002) J. Phys. A: Math. Gen. , vol.35 , pp. 3467-3478
    • Doha, E.H.1
  • 7
    • 0037246330 scopus 로고    scopus 로고
    • Efficient spectral Galerkin-algorithms for direct solution of second-order equations using ultraspherical polynomials
    • Doha, E. H. and Abd-Elhameed, W. M. (2002). Efficient spectral Galerkin-algorithms for direct solution of second-order equations using ultraspherical polynomials. SIAM J. Sci. Comput., 24(2), 548-571.
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 548-571
    • Doha, E.H.1    Abd-Elhameed, W.M.2
  • 8
    • 0029541854 scopus 로고
    • On the Legendre coefficients of the moments of the general-order derivative of an infinitely differentiable function
    • Doha, E. H. and El-Soubhy, S. I. (1995). On the Legendre coefficients of the moments of the general-order derivative of an infinitely differentiable function. Internat. J. Comput. Math., 56(1, 2), 107-122.
    • (1995) Internat. J. Comput. Math. , vol.56 , Issue.1-2 , pp. 107-122
    • Doha, E.H.1    El-Soubhy, S.I.2
  • 10
    • 0031247736 scopus 로고    scopus 로고
    • Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case
    • Godoy, E., Ronveaux, A., Zarzo, A. and Area, I. (1997). Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case. J. Comput. Appl. Math., 84, 257-275.
    • (1997) J. Comput. Appl. Math. , vol.84 , pp. 257-275
    • Godoy, E.1    Ronveaux, A.2    Zarzo, A.3    Area, I.4
  • 11
    • 0002193620 scopus 로고
    • Numerical analysis of spectral methods: Theory and applications
    • Society of Industrial and Applied Mathematics, Philadelphia, PA
    • Gottlieb, D. and Orszag, S. A. (1977). Numerical analysis of spectral methods: Theory and applications. CBMS - NSF Regional Conf. Series in Applied Mathematics, Vol. 26. Society of Industrial and Applied Mathematics, Philadelphia, PA.
    • (1977) CBMS - NSF Regional Conf. Series in Applied Mathematics , vol.26
    • Gottlieb, D.1    Orszag, S.A.2
  • 12
    • 0000036756 scopus 로고
    • A note on the Chebyshev coefficients of the general-order derivative of an infinitely differentiable function
    • Karageorghis, A. (1988). A note on the Chebyshev coefficients of the general-order derivative of an infinitely differentiable function. J. Comput. Appl. Math., 21, 129-132.
    • (1988) J. Comput. Appl. Math. , vol.21 , pp. 129-132
    • Karageorghis, A.1
  • 13
    • 45549111744 scopus 로고
    • A note on the Chebyshev coefficients of the moments of the general-order derivative of infinitely differentiable function
    • Karageorghis, A. (1988). A note on the Chebyshev coefficients of the moments of the general-order derivative of infinitely differentiable function. J. Comput. Appl. Math., 21, 383-386.
    • (1988) J. Comput. Appl. Math. , vol.21 , pp. 383-386
    • Karageorghis, A.1
  • 14
    • 38249010665 scopus 로고
    • Quick construction of recurrence relations for Jacobi coefficients
    • Lewanowicz, S. (1992). Quick construction of recurrence relations for Jacobi coefficients. J. Comput. Appl. Math., 43, 355-372.
    • (1992) J. Comput. Appl. Math. , vol.43 , pp. 355-372
    • Lewanowicz, S.1
  • 17
    • 0040591543 scopus 로고
    • The numerical solution of linear recurrence relations
    • Oliver, J. (1969). The numerical solution of linear recurrence relations. Numer. Math., 11, 349-360.
    • (1969) Numer. Math. , vol.11 , pp. 349-360
    • Oliver, J.1
  • 18
    • 0001324079 scopus 로고
    • On the Legendre coefficients of a general-order derivative of an infinitely differentiable function
    • Phillips, T. N. (1988). On the Legendre coefficients of a general-order derivative of an infinitely differentiable function. IMA. J. Numer. Anal., 8, 455-459.
    • (1988) IMA. J. Numer. Anal. , vol.8 , pp. 455-459
    • Phillips, T.N.1
  • 20
    • 0002857683 scopus 로고
    • Recurrence relations for connection coefficients between two families of orthogonal polynomials
    • Ronveaux, A., Zarzo, A. and Godoy, E. (1995). Recurrence relations for connection coefficients between two families of orthogonal polynomials. J. Comput. Appl. Math., 62, 67-73.
    • (1995) J. Comput. Appl. Math. , vol.62 , pp. 67-73
    • Ronveaux, A.1    Zarzo, A.2    Godoy, E.3
  • 21
    • 0032498758 scopus 로고    scopus 로고
    • Expansions in series of orthogonal polynomials
    • Sánchez-Ruiz, J. and Dehesa, J. S. (1998). Expansions in series of orthogonal polynomials. J. Comput. Appl. Math., 89, 155-170.
    • (1998) J. Comput. Appl. Math. , vol.89 , pp. 155-170
    • Sánchez-Ruiz, J.1    Dehesa, J.S.2
  • 22
    • 0039406287 scopus 로고
    • A modification of Miller's recurrence algorithm
    • Scraton, R. E. (1972). A modification of Miller's recurrence algorithm. BIT, 12, 242-251.
    • (1972) BIT , vol.12 , pp. 242-251
    • Scraton, R.E.1
  • 24
    • 0003503814 scopus 로고    scopus 로고
    • Wolfram Research, Champaign, IL
    • Wolfram Research, Inc. (1999). Mathematica version 4.0. Wolfram Research, Champaign, IL.
    • (1999) Mathematica Version 4.0.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.