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Mittag-Leffler function

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1: 10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
§10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function
The Laplace transform of ϕ ( ρ , β ; z ) can be expressed in terms of the Mittag-Leffler function:
10.46.3 E a , b ( z ) = k = 0 z k Γ ( a k + b ) , a > 0 .
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). …
2: Bibliography P
  • R. B. Paris (2002c) Exponential asymptotics of the Mittag-Leffler function. Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
  • 3: Bibliography W
  • R. Wong and Y. Zhao (2002a) Exponential asymptotics of the Mittag-Leffler function. Constr. Approx. 18 (3), pp. 355–385.
  • 4: Bibliography H
  • H. J. Haubold, A. M. Mathai, and R. K. Saxena (2011) Mittag-Leffler functions and their applications. J. Appl. Math. 2011, pp. Art. ID 298628, 51 pages.
  • 5: 1.10 Functions of a Complex Variable
    Analytic Functions
    §1.10(vi) Multivalued Functions
    §1.10(vii) Inverse Functions
    Mittag-Leffler’s Expansion