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 [[OMEGA].sub.d] = E([R.sup.2]) denotes the average power of desired information signal, while [F.sub.1](a,b,z) and [GAMMA](a) denote the confluent hypergeometric function [10, Eq.(9.210/1)] and Gamma function [10, Eq.
SSC Reception over Kappa-Mu Shadowed Fading Channels in the Presence of Multiple Rayleigh Interferers
with 1F1 being the Kummer confluent hypergeometric function [6].
A New Special Function and Its Application in Probability
We define the confluent hypergeometric function with matrix parameters as
The Second Kummer Function with Matrix Parameters and Its Asymptotic Behaviour
where [beta] - v > (m - 1)/2, [alpha] - v > (m - 1)/2, v > (m - 1)/2,[theta] > 0, [OMEGA] > 0, and [sub.1][F.sub.1] is the confluent hypergeometric function of the first kind of matrix argument (Gupta and Nagar [1]).
Properties of matrix variate confluent hypergeometric function distribution
2 Close-to-convexity of the confluent hypergeometric function
On the Janowski convexity and starlikeness of the confluent hypergeometric function
where [GAMMA](x) is the gamma function, [sub.1][F.sub.1](a, b; x) is the confluent hypergeometric function, [w.sub.0] is the beam waist, p [greater than or equal to] -[absolute value of m] is a real valued parameter, m is the topological charge, p and m together specify the HyG mode, [chi] = [[rho].sup.2]/([w.sup.2.sub.0][[xi] + i]), and [xi] = z/[z.sub.R] with [z.sub.R] = [pi][w.sup.2.sub.0]/[lambda] the Rayleigh range.
Metasurface Synthesis for Time-Harmonic Waves: Exact Spectral and Spatial Methods
then a confluent hypergeometric function can be shown to be a limiting case of a hypergeometric function as follows.
The first negative moment of skew-t and generalized student's t-distributions in the principal value sense
The confluent hypergeometric function of second kind is defined by [9]
Una distribucion generalizada tipo gamma que involucra la funcion hipergeometrica confluente de segunda clase
* Confluent hypergeometric function. This corresponds to v = -[alpha].
Structural and recurrence relations for hypergeometric-type functions by Nikiforov-Uvarov method
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):
An Exponential Family of Lorenz Curves
The results are presented in terms of hypergeometric functions and confluent hypergeometric functions. It is of interest to note that the confluent hypergeometric function, M, yields the prior moment generating function of p from density (1).
Bayesian estimation of population density and visibility
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