Mittag-Leffler expansion
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1: 1.10 Functions of a Complex Variable
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Mittag-Leffler’s Expansion
…2: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
§10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
… ►For exponentially-improved asymptotic expansions in the same circumstances, together with smooth interpretations of the corresponding Stokes phenomenon (§§2.11(iii)–2.11(v)) see Wong and Zhao (1999b) when , and Wong and Zhao (1999a) when . ►The Laplace transform of can be expressed in terms of the Mittag-Leffler function: …This reference includes exponentially-improved asymptotic expansions for when , together with a smooth interpretation of Stokes phenomena. See also Wong and Zhao (2002a), and for further information on the Mittag-Leffler function see Erdélyi et al. (1955, §18.1), Paris and Kaminski (2001, §5.1.4), and Haubold et al. (2011). …3: Bibliography P
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On the use of Hadamard expansions in hyperasymptotic evaluation. I. Real variables.
Proc. Roy. Soc. London Ser. A 457 (2016), pp. 2835–2853.
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On the use of Hadamard expansions in hyperasymptotic evaluation. II. Complex variables.
Proc. Roy. Soc. London Ser. A 457, pp. 2855–2869.
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Error bounds for the uniform asymptotic expansion of the incomplete gamma function.
J. Comput. Appl. Math. 147 (1), pp. 215–231.
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A uniform asymptotic expansion for the incomplete gamma function.
J. Comput. Appl. Math. 148 (2), pp. 323–339.
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Exponential asymptotics of the Mittag-Leffler function.
Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
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4: Bibliography W
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Exponential asymptotics of the Mittag-Leffler function.
Constr. Approx. 18 (3), pp. 355–385.
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On uniform asymptotic expansion of definite integrals.
J. Approximation Theory 7 (1), pp. 76–86.
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Asymptotic expansions of the Kontorovich-Lebedev transform.
Appl. Anal. 12 (3), pp. 161–172.
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Applications of some recent results in asymptotic expansions.
Congr. Numer. 37, pp. 145–182.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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5: Bibliography H
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Expansions for the probability function in series of Čebyšev polynomials and Bessel functions.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 77–80, 96 (Russian).
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Asymptotic expansion of Laplace transforms near the origin.
SIAM J. Math. Anal. 1 (1), pp. 118–130.
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Asymptotic expansion of a class of integral transforms with algebraically dominated kernels.
J. Math. Anal. Appl. 35 (2), pp. 405–433.
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Spherical Bessel expansions of sine, cosine, and exponential integrals.
Appl. Numer. Math. 34 (1), pp. 95–98.
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Mittag-Leffler functions and their applications.
J. Appl. Math. 2011, pp. Art. ID 298628, 51 pages.
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