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Chebyshev-series expansions

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11: 3.11 Approximation Techniques
§3.11(ii) Chebyshev-Series Expansions
Chebyshev Expansions
Calculation of Chebyshev Coefficients
Complex Variables
12: 7.24 Approximations
§7.24(ii) Expansions in Chebyshev Series
13: 7.6 Series Expansions
§7.6 Series Expansions
§7.6(i) Power Series
The series in this subsection and in §7.6(ii) converge for all finite values of | z | .
§7.6(ii) Expansions in Series of Spherical Bessel Functions
7.6.9 erf ( a z ) = 2 z π e ( 1 2 - a 2 ) z 2 n = 0 T 2 n + 1 ( a ) i n ( 1 ) ( 1 2 z 2 ) , - 1 a 1 .
14: 18.3 Definitions
§18.3 Definitions
15: Bibliography R
  • A. Ralston (1965) Rational Chebyshev approximation by Remes’ algorithms. Numer. Math. 7 (4), pp. 322–330.
  • M. Razaz and J. L. Schonfelder (1980) High precision Chebyshev expansions for Airy functions and their derivatives. Technical report University of Birmingham Computer Centre.
  • M. Razaz and J. L. Schonfelder (1981) Remark on Algorithm 498: Airy functions using Chebyshev series approximations. ACM Trans. Math. Software 7 (3), pp. 404–405.
  • E. Ya. Remez (1957) General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.
  • J. Rushchitsky and S. Rushchitska (2000) On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.
  • 16: Bibliography D
  • G. Delic (1979a) Chebyshev expansion of the associated Legendre polynomial P L M ( x ) . Comput. Phys. Comm. 18 (1), pp. 63–71.
  • G. Delic (1979b) Chebyshev series for the spherical Bessel function j l ( r ) . Comput. Phys. Comm. 18 (1), pp. 73–86.
  • P. Dienes (1931) The Taylor Series. Oxford University Press, Oxford.
  • R. B. Dingle (1973) Asymptotic Expansions: Their Derivation and Interpretation. Academic Press, London-New York.
  • J. Dougall (1907) On Vandermonde’s theorem, and some more general expansions. Proc. Edinburgh Math. Soc. 25, pp. 114–132.
  • 17: Bibliography P
  • W. F. Perger, A. Bhalla, and M. Nardin (1993) A numerical evaluator for the generalized hypergeometric series. Comput. Phys. Comm. 77 (2), pp. 249–254.
  • R. Piessens (1984a) Chebyshev series approximations for the zeros of the Bessel functions. J. Comput. Phys. 53 (1), pp. 188–192.
  • R. Piessens and M. Branders (1972) Chebyshev polynomial expansions of the Riemann zeta function. Math. Comp. 26 (120), pp. G1–G5.
  • A. Pinkus and S. Zafrany (1997) Fourier Series and Integral Transforms. Cambridge University Press, Cambridge.
  • P. J. Prince (1975) Algorithm 498: Airy functions using Chebyshev series approximations. ACM Trans. Math. Software 1 (4), pp. 372–379.
  • 18: Bibliography C
  • C. W. Clenshaw (1955) A note on the summation of Chebyshev series. Math. Tables Aids Comput. 9 (51), pp. 118–120.
  • C. W. Clenshaw (1957) The numerical solution of linear differential equations in Chebyshev series. Proc. Cambridge Philos. Soc. 53 (1), pp. 134–149.
  • C. W. Clenshaw (1962) Chebyshev Series for Mathematical Functions. National Physical Laboratory Mathematical Tables, Vol. 5. Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
  • W. J. Cody (1965b) Chebyshev polynomial expansions of complete elliptic integrals. Math. Comp. 19 (90), pp. 249–259.
  • J. P. Coleman and A. J. Monaghan (1983) Chebyshev expansions for the Bessel function J n ( z ) in the complex plane. Math. Comp. 40 (161), pp. 343–366.