References
- Abramowitz M. Stegun I. A. (Eds.) (1970) Handbook of Mathematical Functions Appl. Maths Series Vol. 55 National Bureau of Standards New York
- Canuto C. Hussaini M. Y. Quarteroni A. Zang T. A. (1988) Spectral Methods in Fluid Dynamics Springer Berlin
- Doha , E. H. (1991) . The coefficients of differentiated expansions and derivatives of ultraspherical polynomials . J. Comput. Math. Appl. , 21 : 115 – 122 .
- 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 .
- 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 .
- Doha , E. H. (2002) . On the coefficients of differentiated expansions and derivatives of jacobi polynomials . J. Phys. A: Math. Gen. , 35 : 3467 – 3478 .
- 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 .
- 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 .
- Fox L. Parker I. B. (1972) Chebyshev Polynomials in Numerical Analysis Oxford University Press London
- 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 .
- Gottlieb D. 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
- 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 .
- 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 .
- Lewanowicz , S. (1992) . Quick construction of recurrence relations for Jacobi coefficients . J. Comput. Appl. Math. , 43 : 355 – 372 .
- Luke Y. (1969) The Special Functions and Their Approximations Vol. 1 Academic Press New York
- Nikiforov A. F. Uvarov V. B. (1988) Special Functions in Mathematical Physics Birkhauser Basel
- Oliver , J. (1969) . The numerical solution of linear recurrence relations . Numer. Math. , 11 : 349 – 360 .
- 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 .
- Rainville E. D. (1960) Special Functions The Macmillan Company New York
- 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 .
- Sánchez-Ruiz , J. and Dehesa , J. S. (1998) . Expansions in series of orthogonal polynomials . J. Comput. Appl. Math. , 89 : 155 – 170 .
- Scraton , R. E. (1972) . A modification of Miller's recurrence algorithm . BIT , 12 : 242 – 251 .
- Wimp J. (1984) Computation with Recurrence Relations Pitman Advanced Publishing Program London
- Wolfram Research, Inc. (1999) Mathematica version 4.0 Wolfram Research Champaign IL