limit of Jacobi polynomials
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11: 18.26 Wilson Class: Continued
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18.26.7
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12: 18.18 Sums
§18.18 Sums
… ►Jacobi
… ►Jacobi
… ►Jacobi
… ►See also (18.38.3) for a finite sum of Jacobi polynomials. …13: Bibliography R
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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials.
Canad. J. Math. 33 (4), pp. 915–928.
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The Associated Classical Orthogonal Polynomials.
In Special Functions 2000: Current Perspective and Future
Directions (Tempe, AZ),
NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 255–279.
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Normal limit theorems for symmetric random matrices.
Probab. Theory Related Fields 112 (3), pp. 411–423.
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Relationships between the zeros, weights, and weight functions of orthogonal polynomials: Derivative rule approach to Stieltjes and spectral imaging.
Computing in Science and Engineering 23 (3), pp. 56–64.
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Applied Bessel Functions.
Dover Publications Inc., New York.
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14: 18.19 Hahn Class: Definitions
§18.19 Hahn Class: Definitions
… ►In addition to the limit relations in §18.7(iii) there are limit relations involving the further families in the Askey scheme, see §§18.21(ii) and 18.26(ii). The Askey scheme, depicted in Figure 18.21.1, gives a graphical representation of these limits. … ►Hahn, Krawtchouk, Meixner, and Charlier
►Tables 18.19.1 and 18.19.2 provide definitions via orthogonality and standardization (§§18.2(i), 18.2(iii)) for the Hahn polynomials , Krawtchouk polynomials , Meixner polynomials , and Charlier polynomials . …15: 29.6 Fourier Series
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►With , as in (29.2.5), we have
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►In addition, if satisfies (29.6.2), then (29.6.3) applies.
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►Consequently, reduces to a Lamé polynomial; compare §§29.12(i) and 29.15(i).
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►Here is as in §22.2, and
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29.6.53
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16: Bibliography F
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II.
J. Math. Anal. Appl. 7 (3), pp. 440–451.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order.
J. Math. Anal. Appl. 6 (3), pp. 394–403.
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Application of the -function theory of Painlevé equations to random matrices: , the JUE, CyUE, cJUE and scaled limits.
Nagoya Math. J. 174, pp. 29–114.
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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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Asymptotic expansions of the Lebesgue constants for Jacobi series.
Pacific J. Math. 122 (2), pp. 391–415.
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17: Bibliography D
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On the real roots of Euler polynomials.
Monatsh. Math. 106 (2), pp. 115–138.
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On multiple zeros of Bernoulli polynomials.
Acta Arith. 134 (2), pp. 149–155.
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Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets.
SIAM J. Math. Anal. 30 (5), pp. 1029–1056.
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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results.
SIAM J. Math. Anal. 9 (1), pp. 76–86.
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18: 35.7 Gaussian Hypergeometric Function of Matrix Argument
19: Bibliography C
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Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial
as the index and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials.
Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.
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A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
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Sur la fonction qui détermine la totalité des nombres premiers inférieurs à une limite donnée.
Mem. Ac. Sc. St. Pétersbourg 6, pp. 141–157.
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A Bernstein-type inequality for the Jacobi polynomial.
Proc. Amer. Math. Soc. 121 (3), pp. 703–709.
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Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems.
SIGMA Symmetry Integrability Geom. Methods Appl. 9, pp. Paper 042, 26.
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