generalized Bessel polynomials
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1: 18.34 Bessel Polynomials
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βΊ
§18.34(i) Definitions and Recurrence Relation
… βΊ
18.34.1
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βΊOften only the polynomials (18.34.2) are called Bessel
polynomials, while the polynomials (18.34.1) and (18.34.3) are called generalized Bessel polynomials.
Sometimes the polynomials
are called reverse Bessel polynomials.
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βΊ
18.34.7_1
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2: Bibliography D
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βΊ
On the zeros of generalized Bessel polynomials. I.
Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 1–13.
βΊ
On the zeros of generalized Bessel polynomials. II.
Nederl. Akad. Wetensch. Indag. Math. 84 (1), pp. 14–25.
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βΊ
Uniform asymptotic expansions for the reverse generalized Bessel polynomials, and related functions.
SIAM J. Math. Anal. 32 (5), pp. 987–1013.
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3: Bibliography W
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βΊ
Asymptotic expansions of the generalized Bessel polynomials.
J. Comput. Appl. Math. 85 (1), pp. 87–112.
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4: 18.15 Asymptotic Approximations
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βΊ
18.15.19
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5: Bibliography L
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βΊ
Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and Buchholz polynomials.
J. Math. Anal. Appl. 239 (2), pp. 457–477.
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6: 35.9 Applications
§35.9 Applications
βΊIn multivariate statistical analysis based on the multivariate normal distribution, the probability density functions of many random matrices are expressible in terms of generalized hypergeometric functions of matrix argument , with and . … βΊThese references all use results related to the integral formulas (35.4.7) and (35.5.8). … βΊIn chemistry, Wei and Eichinger (1993) expresses the probability density functions of macromolecules in terms of generalized hypergeometric functions of matrix argument, and develop asymptotic approximations for these density functions. βΊIn the nascent area of applications of zonal polynomials to the limiting probability distributions of symmetric random matrices, one of the most comprehensive accounts is Rains (1998).7: 18.3 Definitions
§18.3 Definitions
… βΊFor expressions of ultraspherical, Chebyshev, and Legendre polynomials in terms of Jacobi polynomials, see §18.7(i). …For explicit power series coefficients up to for these polynomials and for coefficients up to for Jacobi and ultraspherical polynomials see Abramowitz and Stegun (1964, pp. 793–801). … βΊBessel polynomials
βΊBessel polynomials are often included among the classical OP’s. …8: 10.49 Explicit Formulas
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βΊ
§10.49(i) Unmodified Functions
… βΊ§10.49(ii) Modified Functions
… βΊ is sometimes called the Bessel polynomial of degree . For a survey of properties of these polynomials and their generalizations see Grosswald (1978). … …9: 18.18 Sums
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βΊ
18.18.27
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10: 18.11 Relations to Other Functions
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βΊ
18.11.6
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