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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where [PHI]([alpha]; [beta]; *) is the type 1 confluent hypergeometric function.
1] X/d) by the confluent hypergeometric function of matrix argument [sub.
Several important functions are special cases of the confluent hypergeometric function.
A gamma type distribution involving a confluent hypergeometric function of the second kind*
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).
1] represents the confluent hypergeometric function.
Based on the beta function, the Gauss hypergeometric function, denoted by F(a, b; c; z), and the confluent hypergeometric function, denoted by [PHI](b; c; z), for Re(c) > Re(b) > 0, are defined as (see Luke [1]),
in terms of the confluent hypergeometric function of the first kind or Kummer function.
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