## Orthogonal rational functions on a semi-infinite interval.(English)Zbl 0614.42013

The author obtains a sequence of orthogonal functions on [0,$$\infty [$$ by taking a Möbius transform in the argument of the usual Chebyshev polynomials. He discusses their applicability to expansions of functions, solution of eigenproblems, and boundary value problems in seven numerical examples.
Reviewer: J.Karlsson

### MSC:

 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 41A20 Approximation by rational functions
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### References:

 [1] Boyd, J.P., J. comput. phys., 69, 112-142, (1987) [2] Grosch, C.E.; Orszag, S.A., J. comp. phys., 25, 273, (1977) [3] Boyd, J.P., J. comput. phys., 45, 43, (1982) [4] Boyd, J.P., J. comput. phys., 54, 382, (1984) [5] Boyd, J.P., J. comput. phys., 57, 454, (1985) [6] Boyd, J.P., J. comput. phys., 64, 266, (1986) [7] Norton, H.J., Comput. J., 7, 76, (1964) [8] Boyd, J.P., Physica D, 21, 227, (1986) [9] Gottlieb, D.; Orszag, S.A., Numerical analysis of spectral methods: theory and applications, (1977), SIAM Philadelphia · Zbl 0412.65058 [10] Cain, A.B.; Ferziger, J.H.; Reynolds, W.C., J. comput. phys., 56, 272, (1984) [11] Boyd, J.P., Monthly weather rev., 106, 1192, (1978) [12] Pedlosky, J., Geophysical fluid dynamics, (1979), Springer-Verlag New York · Zbl 0429.76001 [13] Boyd, J.P., J. math. phys., 19, 1445, (1978) [14] Stenger, F., SIAM rev., 23, 165, (1981) [15] Nayfeh, A.H., Perturbation methods, (1973), Wiley New York · Zbl 0375.35005 [16] Canuto, C.; Quarteroni, A., J. comput. phys., 60, 315, (1985) [17] Boyd, J.P., J. sci. comput., 1, 183, (1986) [18] Gary, J.; Helgason, R., J. comput. phys., 5, 169, (1970) [19] Trefethen, L.N.; Trummer, M.R., SIAM J. numer. anal., (1986), in press
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