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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Taylor expansion is employed to linearize the nonlinear confluent hypergeometric function. Accordingly, a closed-form expression can be derived in the E-step and the complexity of the proposed algorithm can be significantly reduced.
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.
The inverse symbolic calculator is unable to give us the representation of 0.97210699*** using standard special functions, but we have tried to give its representation using error function representation as hypergeometric function [6]; we have
where [F.sub.c] (z) is the Fresnel cosine integral and [sub.1][F.sub.2] is the hypergeometric function defined by
Here, [F.sub.1]([alpha], [beta], [beta]', [gamma]; x; y) is the Appel hypergeometric function with two variables.
where [psi](*) is the degenerate hypergeometric function (see, e.g., [21]), and C is a constant to be determined.
Equation (13) differs from the generalized hypergeometric function [sub.p][F.sub.q](z) defined in (9) only by a constant multiplier.
For any real or complex numbers a, b and c (c [not equal to] [Z.sup.-.sub.0] := {0,-1,-2,...}), the Gaussian hypergeometric function is defined by
[sub.1][F.sub.l] (a;b;c) represents the confluent hypergeometric function of first kind [36, Eq.