2] = 0) as a hypergeometric function
C]([alpha], [beta];x) is the confluent hypergeometric function
defined by the series :
By using the Gaussian hypergeometric function
given by [sub.
Generalized ordinary hypergeometric function
of one variable is defined by
The hypergeometric function
and complete elliptic integrals.
In this case the integral can be expressed (in a very complicated way) in terms of the Appell hypergeometric function
(Appell, 1925), which is a function of two variables that can be represented by the following integral (see Bailey, 1934):
Srivastava, Some sublasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function
1]([alpha], [beta]; [gamma]; x) denotes the Gauss hypergeometric function
of the argument x.
i) Hypergeometric function
: Gauss has introduced the hypergeometric function
Gauss (1777-1855) and Johann Friedrich Pfaff (1765-1825), who developed the hypergeometric function
, the corner-stone of special functions, and the prerequisite for q-hypergeometric functions
The Gini index of the exponential hierarchy can be expressed in terms of the confluent hypergeometric function
, whose integral representation is given by (b [greater than] a):
It is of interest to note that the confluent hypergeometric function
, M, yields the prior moment generating function of p from density (1).