asymptotics of Laguerre polynomials
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1: 18.29 Asymptotic Approximations for -Hahn and Askey–Wilson Classes
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βΊFor a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006).
βΊFor asymptotic approximations to the largest zeros of the -Laguerre and continuous -Hermite polynomials see Chen and Ismail (1998).
2: 18.15 Asymptotic Approximations
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§18.15(iv) Laguerre
… βΊHere denotes the Bessel function (§10.2(ii)), denotes its envelope (§2.8(iv)), and is again an arbitrary small positive constant. … βΊ
18.15.22
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18.15.23
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βΊFor asymptotic approximations of Jacobi, ultraspherical, and Laguerre polynomials in terms of Hermite polynomials, see López and Temme (1999a).
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3: Bibliography T
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Laguerre polynomials: Asymptotics for large degree.
Technical report
Technical Report AM-R8610, CWI, Amsterdam, The Netherlands.
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Asymptotic estimates for Laguerre polynomials.
Z. Angew. Math. Phys. 41 (1), pp. 114–126.
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4: 18.16 Zeros
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Asymptotic Behavior
… βΊLastly, in view of (18.7.19) and (18.7.20), results for the zeros of lead immediately to results for the zeros of . …5: Bibliography D
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Strong and ratio asymptotics for Laguerre polynomials revisited.
J. Math. Anal. Appl. 403 (2), pp. 477–486.
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6: Bibliography
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Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters.
J. Math. Anal. Appl. 416 (1), pp. 52–80.
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7: Bibliography F
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Uniform asymptotic expansions of Laguerre polynomials.
SIAM J. Math. Anal. 19 (5), pp. 1232–1248.
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8: 18.24 Hahn Class: Asymptotic Approximations
§18.24 Hahn Class: Asymptotic Approximations
… βΊFor an asymptotic expansion of as , with fixed, see Li and Wong (2001). … βΊApproximations in Terms of Laguerre Polynomials
… βΊThese approximations are in terms of Laguerre polynomials and hold uniformly for . …Similar approximations are included for Jacobi, Krawtchouk, and Meixner polynomials.9: Bibliography G
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Asymptotics and bounds for the zeros of Laguerre polynomials: A survey.
J. Comput. Appl. Math. 144 (1-2), pp. 7–27.
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10: 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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