The functions 
and 
are used extensively in
statistics as the probability integrals of the gamma distribution; see
Johnson et al. (1994, pp. 337–414). Particular forms are the chi-square
distribution functions; see Johnson et al. (1994, pp. 415–493).
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).
