►Incomplete Airy functions are defined by the contour integral (9.5.4) when one of the integration limits is replaced by a variable real or complex parameter.
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►The functions and are used extensively in statistics as the probability integrals of the gamma distribution; see Johnson et al. (1994, pp. 337–414).
…The function and its normalization play a similar role in statistics in connection with the beta distribution; see Johnson et al. (1995, pp. 210–275).
In queueing theory the Erlang loss function is used, which can be expressed in terms of the reciprocal of ; see Jagerman (1974) and Cooper (1981, pp. 80, 316–319).
►The function appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)).
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►For a generalization of the incomplete gamma function, including asymptotic approximations, see Chaudhry and Zubair (1994, 2001) and Chaudhry et al. (1996).
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