confluent hypergeometric function


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confluent hypergeometric function

[kən′flü·ənt ¦hī·pər‚jē·ə¦me‚trik ′fəŋk·shən]
(mathematics)
A solution to differential equation z (d 2 w/dz 2) + (ρ-z)(dw/dz)-α w = 0.
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1] is the confluent hypergeometric function (Abramowitz and Stegun[?
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).
in terms of the confluent hypergeometric function of the first kind or Kummer function.
As particular cases of the confluent hypergeometric function U(a, c, z) we have several special functions of importance.
This gives an expansion analogous to the Poincare-type expansion, but including confluent hypergeometric functions instead of inverse powers of z as asymptotic sequence.
The purpose of this paper is to analyze some features of this modification, namely the convergence properties of the modified asymptotic series and some techniques that can be used to compute the confluent hypergeometric functions involved in the approximation.
These integrals can be written as confluent hypergeometric functions, by virtue of the integral representation[1, Eq.
Using the relation between the confluent hypergeometric function and the generalized Laguerre polynomials [L.
Some useful systems of coherent states can be defined [3] by using these relations, the confluent hypergeometric function
z]; Rosenbloom [12], who discussed the angular distribution of zeros using potential theory, and applied his work to the sub-class of confluent hypergeometric functions; Erdos and Turan [4], who used minimization techniques to discuss angular distributions of zeros; Newman and Rivlin [7, 8], who related the work of Szego to the Central Limit Theorem; Edrei, Saff and Varga [3], who gave a thorough analysis for the family of Mittag-Leffler functions; Carpenter, Varga and Waldvogel [2], who refined the work of Szego; Norfolk [9, 10], who refined the work of Rosenbloom on the confluent hypergeometric functions and a related set of integral transforms.
Provides introductory material to required mathematical topics such as complex numbers, Laplace and Fourier transforms, matrix algebra, confluent hypergeometric functions, digamma functions, and Bessel functions.