- Andrews , G. E. , Askey , R. and Roy , R. 1999 . Special Functions , UK : Camb. Univ. Press .
- Ben-yu , G. 1998 . Gegenbauer approximation and its applications to differential equations on the whole line . J. Math. Anal. Applics. , 226 : 180 – 206 .
- Canuto , C. , Hussaini , M. Y. , Quarteroni , A. and Zang , T. A. 1988 . Spectral Methods in Fluid Dynamics , Berlin : Springer .
- Coutsias , E. A. , Hagstrom , T. and Torres , D. 1996 . An efficient spectral method for ordinary differentialequations with rational fonction coefficients . Math. Comp. , 65 (214) : 611 – 635 .
- Doha , E. H. 1990 . An accurate solution of parabolic equations by expansion in ultraspherical polynomials . Computers Math. Applic. , 19 (4) : 75 – 88 .
- Doha , E. H. 1991 . The coefficients of differentiated expansions and derivatives of ultraspherical polynomials . Computers Math. Applic. , 21 (2-3) : 115 – 122 .
- Doha , E. H. 2000 . The coefficients of differentiated expansions of double and triple ultraspherical polynomials . Annales Univ. Sci. Budapest., Sect. Comp. , 19 : 57 – 73 .
- Doha , E. H. 2002 . On the coefficients of integrated expansions and integrals of ultraspherical polynomials andtheir applications for solving differential equations . J. Comput. Appl. Math. , 139 : 275 – 298 .
- Doha , E. H. 2002 . On the coefficients of differentiated expansions and derivatives of Jacobi polynomials . J. Phys. A: Math. Gen. , 35 : 1 – 12 .
- Doha , E. H. and Al-Kholi , F. M. R. 2001 . An efficient double Legendre spectral method for parabolic andelliptic partial differential equations . Intern. J. Computer Math. , 78 : 413 – 432 .
- Doha , E. H. and Helal , M. A. 1997 . An accurate double Chebyshev spectral approximation for parabolic partialdifferential equations . J. Egypt. Math. Soc. , 5 (1) : 83 – 101 .
- Gottlieb , D. and Orszag , S. A. 1977 . Numerical analysis of spectral methods: Theory and applications , CBMS-NSF Regional Conference Series in Applied Mathematics 26 Philadelphia
- Haidvogel , D. B. and Zang , T. 1979 . The accurate solution of Poisson's equation by Chebyshev polynomials . J. Comput. Phys. , 30 : 167 – 180 .
- Helal , M. A. 2001 . A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamicalapplication . Chaos, Solitons and Fractals , 12 : 943 – 950 .
- Karageorghis , A. 1988 . A note on the Chebyshev coefficients of the general-order derivative of an infinitelydifferentiable function . J. Comput. Appl. Math. , 21 : 129 – 132 .
- Karageorghis , A. and Phillips , T. N. 1989 and 1992 . On the coefficients of differentiated expansions ofultraspherical polynomials. ICASE Report No. 89-65, NASA Langley Research Center, Hampton, VA and Appl . Num. Math. , 9 : 133 – 141 .
- Luke , Y. 1975 . Mathematical Functions and their Approximations , New-York : Academic Press .
- Phillips , T. N. 1988 . On the Legendre coefficients of a general order derivative of an infinitely differentiatedfunction . IMA J. Numer. Anal. , 8 : 455 – 459 .
- Phillips , T. N. and Karageorghis , A. 1990 . On the coefficients of integrated expansions of ultrasphericalpolynomials . SIAM J. Numer. Anal. , 27 : 823 – 830 .
- Siyyam , H. I. and Syam , M. I. 1997 . An accurate solution of the Poisson equation by the Chebyshev-Taumethod . J. Comput. Appl. Math. , 85 : 1 – 10 .
- Szegö , G. 1985 . Orthogonal Polynomials . Am. Math. Soc. Colloq. Pub. , : 23
- Voigt , R. G. , ed. 1984 . Spectral Methods for Partial Differential Equations , Philadelphia : SIAM .
- Watson , G. N. 1925 . A note on generalized hypergeometric series . Proc. London Math. Soc. , 23 (2) : xiii – xv . (Records for 8 Nov. 1925)
Integral Transforms and Special Functions
Volume 14, 2003 - Issue 1