in series of Chebyshev polynomials
(0.008 seconds)
11—20 of 29 matching pages
11: 18.2 General Orthogonal Polynomials
§18.2(vi) Zeros
… ►This says roughly that the series (18.2.25) has the same pointwise convergence behavior as the same series with , a Chebyshev polynomial of the first kind, see Table 18.3.1. … ►for in the support of the orthogonality measure and such that the series in (18.2.41) converges absolutely for all these . … ►In fact, these are the only OP’s which are Sheffer polynomials (with Krawtchouk polynomials being only a finite system) … ►For other examples of Sheffer polynomials, not in DLMF, see Roman (1984). …12: 7.24 Approximations
§7.24(ii) Expansions in Chebyshev Series
►Luke (1969b, pp. 323–324) covers and for (the Chebyshev coefficients are given to 20D); and for (the Chebyshev coefficients are given to 20D and 15D, respectively). Coefficients for the Fresnel integrals are given on pp. 328–330 (20D).
Bulirsch (1967) provides Chebyshev coefficients for the auxiliary functions and for (15D).
Schonfelder (1978) gives coefficients of Chebyshev expansions for on , for on , and for on (30D).
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
13: 6.20 Approximations
§6.20(ii) Expansions in Chebyshev Series
… ►Luke and Wimp (1963) covers for (20D), and and for (20D).
Luke (1969b, pp. 41–42) gives Chebyshev expansions of , , and for , . The coefficients are given in terms of series of Bessel functions.
Luke (1969b, pp. 321–322) covers and for (the Chebyshev coefficients are given to 20D); for (20D), and for (15D). Coefficients for the sine and cosine integrals are given on pp. 325–327.
Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric -function (§13.2(i)) from which Chebyshev expansions near infinity for , , and follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the functions. If the scheme can be used in backward direction.
14: 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 . ►§7.6(ii) Expansions in Series of Spherical Bessel Functions
… ►15: 11.15 Approximations
§11.15(i) Expansions in Chebyshev Series
►Luke (1975, pp. 416–421) gives Chebyshev-series expansions for , , , and , , for ; , , , and , , ; the coefficients are to 20D.
MacLeod (1993) gives Chebyshev-series expansions for , , , and , , ; the coefficients are to 20D.
§11.15(ii) Rational and Polynomial Approximations
►Newman (1984) gives polynomial approximations for for , , and rational-fraction approximations for for , . The maximum errors do not exceed 1.2×10⁻⁸ for the former and 2.5×10⁻⁸ for the latter.