continuous%20dual%20Hahn%20polynomials
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11—20 of 354 matching pages
11: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Continuous Hahn polynomials.
J. Phys. A 18 (16), pp. L1017–L1019.
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Continuous
-Hermite Polynomials when
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In
-series and Partitions (Minneapolis, MN, 1988),
IMA Vol. Math. Appl., Vol. 18, pp. 151–158.
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12: 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
§18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
►Ismail (1986) gives asymptotic expansions as , with and other parameters fixed, for continuous -ultraspherical, big and little -Jacobi, and Askey–Wilson polynomials. …For Askey–Wilson the leading term is given by … ►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006). ►For asymptotic approximations to the largest zeros of the -Laguerre and continuous -Hermite polynomials see Chen and Ismail (1998).13: 18.19 Hahn Class: Definitions
§18.19 Hahn Class: Definitions
… ►Hahn class (or linear lattice class). These are OP’s where the role of is played by or or (see §18.1(i) for the definition of these operators). The Hahn class consists of four discrete and two continuous families.
Continuous Hahn
… ► …14: Bibliography F
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Multivariate Calculation. Use of the Continuous Groups.
Springer Series in Statistics, Springer-Verlag, New York.
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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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15: 18.28 Askey–Wilson Class
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§18.28(v) Continuous -Ultraspherical Polynomials
… ►§18.28(vi) Continuous -Hermite Polynomials
… ►§18.28(vii) Continuous -Hermite Polynomials
… ►For continuous -Hermite polynomials the orthogonality measure is not unique. … ►§18.28(ix) Continuous -Jacobi Polynomials
…16: 8 Incomplete Gamma and Related
Functions
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17: 28 Mathieu Functions and Hill’s Equation
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18: 36.5 Stokes Sets
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36.5.4
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36.5.7
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►For the second sheet is generated by a second solution of (36.5.6)–(36.5.9), and for it is generated by the roots of the polynomial equation
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►In Figures 36.5.1–36.5.6 the plane is divided into regions by the dashed curves (Stokes sets) and the continuous curves (bifurcation sets).
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19: Wolter Groenevelt
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►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials.
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