asymptotic%20expansion
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1: 9.9 Zeros
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§9.9(iv) Asymptotic Expansions
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9.9.6
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9.9.18
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9.9.19
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βΊFor error bounds for the asymptotic expansions of , , , and see Pittaluga and Sacripante (1991), and a conjecture given in Fabijonas and Olver (1999).
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2: 10.75 Tables
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Olver (1960) tabulates , , , , , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as ; see §10.21(viii), and more fully Olver (1954).
Olver (1960) tabulates , , , , , , 8D. Also included are tables of the coefficients in the uniform asymptotic expansions of these zeros and associated values as .
3: Bibliography D
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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4: Bibliography N
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Applicable Anal. 39 (4), pp. 249–263.
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On an asymptotic expansion of the Kontorovich-Lebedev transform.
Methods Appl. Anal. 3 (1), pp. 98–108.
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Error bounds for the asymptotic expansion of the Hurwitz zeta function.
Proc. A. 473 (2203), pp. 20170363, 16.
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Uniform asymptotic expansion for the incomplete beta function.
SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.
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Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function.
Appl. Anal. Discrete Math. 7 (1), pp. 161–179.
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5: Bibliography S
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Uniform asymptotic expansions of modified Mathieu functions.
J. Reine Angew. Math. 247, pp. 1–17.
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Asymptotic expansions of Mellin transforms and analogues of Watson’s lemma.
SIAM J. Math. Anal. 16 (4), pp. 896–906.
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A simple approach to asymptotic expansions for Fourier integrals of singular functions.
Appl. Math. Comput. 216 (11), pp. 3378–3385.
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Uniform asymptotic expansions of Hermite polynomials.
M. Phil. thesis, City University of Hong Kong.
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6: 12.11 Zeros
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12.11.9
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7: 28.16 Asymptotic Expansions for Large
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28.16.1
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8: 2.11 Remainder Terms; Stokes Phenomenon
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