generalized Bessel polynomials
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11: 18.10 Integral Representations
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18.10.9
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12: 10.59 Integrals
§10.59 Integrals
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10.59.1
►where is the Legendre polynomial (§18.3).
►For an integral representation of the Dirac delta in terms of a product of spherical Bessel functions of the first kind see §1.17(ii), and for a generalization see Maximon (1991).
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13: 18.12 Generating Functions
14: 35.1 Special Notation
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►Related notations for the Bessel functions are (Faraut and Korányi (1994, pp. 320–329)), (Terras (1988, pp. 49–64)), and (Faraut and Korányi (1994, pp. 357–358)).
15: 16.18 Special Cases
§16.18 Special Cases
►The and functions introduced in Chapters 13 and 15, as well as the more general functions introduced in the present chapter, are all special cases of the Meijer -function. … ►
16.18.1
►As a corollary, special cases of the and functions, including Airy functions, Bessel functions, parabolic cylinder functions, Ferrers functions, associated Legendre functions, and many orthogonal polynomials, are all special cases of the Meijer -function.
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16: 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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Work Group of Computational Mathematics, University of Kassel, Germany.
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Generalized incomplete gamma functions with applications.
J. Comput. Appl. Math. 55 (1), pp. 99–124.
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Properties of generalized Freud polynomials.
J. Approx. Theory 225, pp. 148–175.
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On a generalization of the generating function for Gegenbauer polynomials.
Integral Transforms Spec. Funct. 24 (10), pp. 807–816.
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17: Bibliography Z
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On the Computation of Zeros of Bessel and Bessel-related Functions.
In Proceedings of the Sixth International Colloquium on
Differential Equations (Plovdiv, Bulgaria, 1995), D. Bainov (Ed.),
Utrecht, pp. 409–416.
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Distribution Theory and Transform Analysis, An Introduction and Generalized Functions with Applications.
Dover, New York.
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“Hidden symmetry” of Askey-Wilson polynomials.
Theoret. and Math. Phys. 89 (2), pp. 1146–1157.
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On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval.
J. Approx. Theory 94 (1), pp. 73–106.
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Generalized Watson Transforms and Applications to Group Representations.
Ph.D. Thesis, University of Vermont, Burlington,VT.
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18: 8.7 Series Expansions
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8.7.6
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