Szeg%C5%91%E2%80%93Askey%20polynomials
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21—30 of 342 matching pages
21: 25.16 Mathematical Applications
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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Numerical evaluation of the elliptic integral of the third kind.
Math. Comp. 19 (91), pp. 494–496.
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A uniform asymptotic expansion of the Jacobi polynomials with error bounds.
Canad. J. Math. 37 (5), pp. 979–1007.
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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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23: Bibliography D
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Irreducibility of certain generalized Bernoulli polynomials belonging to quadratic residue class characters.
J. Number Theory 25 (1), pp. 72–80.
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Theta functions and non-linear equations.
Uspekhi Mat. Nauk 36 (2(218)), pp. 11–80 (Russian).
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Error analysis in a uniform asymptotic expansion for the generalised exponential integral.
J. Comput. Appl. Math. 80 (1), pp. 127–161.
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Uniform asymptotic expansions for Charlier polynomials.
J. Approx. Theory 112 (1), pp. 93–133.
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Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
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24: Bibliography W
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Global asymptotics of the Meixner polynomials.
Asymptotic Analysis 75 (3-4), pp. 211–231.
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Asymptotics of orthogonal polynomials via recurrence relations.
Anal. Appl. (Singap.) 10 (2), pp. 215–235.
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Uniform asymptotic expansion of via a difference equation.
Numer. Math. 91 (1), pp. 147–193.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Hypergeometric Series, Recurrence Relations and Some New Orthogonal Polynomials.
Ph.D. Thesis, University of Wisconsin, Madison, WI.
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25: 23.21 Physical Applications
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►For applications to soliton solutions of the Korteweg–de Vries (KdV) equation see McKean and Moll (1999, p. 91), Deconinck and Segur (2000), and Walker (1996, §8.1).
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26: 1.14 Integral Transforms
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27: 32.8 Rational Solutions
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►where the are monic polynomials (coefficient of highest power of is ) satisfying
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►Next, let be the polynomials defined by for , and
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►where and are polynomials of degree , with no common zeros.
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►where and are polynomials of degrees and , respectively, with no common zeros.
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►where , are constants, and , are polynomials of degrees and , respectively, with no common zeros.
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28: Richard A. Askey
Profile
Richard A. Askey
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►Richard A. Askey (b.
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►Askey received his Ph.
… Wilson), introduced the Askey-Wilson polynomials.
…Another significant contribution was the Askey-Gasper inequality for Jacobi polynomials which was published in Positive Jacobi polynomial sums. II (with G.
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29: 8.23 Statistical Applications
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►In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of ; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).
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30: 26.13 Permutations: Cycle Notation
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