hypergeometric function


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hypergeometric function

[‚hī·pər‚jē·ə′me·trik ′fəŋk·shən]
(mathematics)
A function which is a solution to the hypergeometric equation and obtained as an infinite series expansion.
References in periodicals archive ?
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, Adv.
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).