polynomials%20orthogonal%20on%20the%20unit%20circle
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21—30 of 695 matching pages
21: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory.
American Mathematical Society Colloquium Publications, Vol. 54, American Mathematical Society, Providence, RI.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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22: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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On the coefficients in the recursion formulae of orthogonal polynomials.
Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.
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23: 18.21 Hahn Class: Interrelations
§18.21 Hahn Class: Interrelations
►§18.21(i) Dualities
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… ►Meixner Laguerre
…24: 25.20 Approximations
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Cody et al. (1971) gives rational approximations for in the form of quotients of polynomials or quotients of Chebyshev series. The ranges covered are , , , . Precision is varied, with a maximum of 20S.
25: 7.24 Approximations
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Hastings (1955) gives several minimax polynomial and rational approximations for , and the auxiliary functions and .
Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Cody et al. (1970) gives minimax rational approximations to Dawson’s integral (maximum relative precision 20S–22S).
26: 23 Weierstrass Elliptic and Modular
Functions
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27: 18.40 Methods of Computation
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§18.40(i) Computation of Polynomials
►Orthogonal polynomials can be computed from their explicit polynomial form by Horner’s scheme (§1.11(i)). …For applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev. … … ►Results of low ( to decimal digits) precision for are easily obtained for to . …28: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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Exceptional orthogonal polynomials.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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29: 28 Mathieu Functions and Hill’s Equation
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30: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Orthogonal polynomials, duality and association schemes.
SIAM J. Math. Anal. 13 (4), pp. 656–663.
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Orthogonal Polynomials for Exponential Weights.
CMS Books in Mathematics/Ouvrages de Mathématiques de la
SMC, 4, Springer-Verlag, New York.
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Approximation of orthogonal polynomials in terms of Hermite polynomials.
Methods Appl. Anal. 6 (2), pp. 131–146.
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