scholarly journals Multiple-term approximations for Appell's F1 function

1997 ◽  
Vol 39 (1) ◽  
pp. 135-148
Author(s):  
Magdi A. El-Gabali
Keyword(s):  
Error Analysis ◽  
Closed Form ◽  
Wide Class ◽  
Special Functions ◽  
Form Error ◽  
Novel Technique ◽  
Highly Efficient ◽  
Image Position

AbstractIn this paper computational issues of Appell's F1 functionare addressed. A novel technique is used in the derivation of highly efficient multiple-term approximations of this function (including asymptotic ones). Simple structured single- and double-term approximations, as the first two candidates of this multiple-term representa-tion, are developed in closed form. Error analysis shows that- the developed algorithms are superior to existing approximations for the same number of terms. The formulation presented is highly efficient and could be extended to a wide class of special functions.

Closed-Form Error Analysis of AF-CARQ with CSI-Assisted Relay over Nakagami- $$m$$ m Fading Channels

2014 ◽  
Vol 78 (1) ◽  
pp. 629-647 ◽  
Author(s):  
Suoping Li ◽  
Kun Wu ◽  
Yongqiang Zhou ◽  
Zufang Dou
Keyword(s):  
Error Analysis ◽  
Closed Form ◽  
Fading Channels ◽  
Form Error

scholarly journals Efficient multiple-term approximations for the generalised elliptic-type integrals

1997 ◽  
Vol 38 (3) ◽  
pp. 411-426 ◽  
Author(s):  
M. El-Gabali
Keyword(s):  
Entire Range ◽  
Special Functions ◽  
Gauss Hypergeometric Function ◽  
Elliptic Type ◽  
Closed Form Solutions ◽  
Novel Technique ◽  
Single Term ◽  
Type Integral ◽  
Image Position ◽  
Term Approximation

AbstractThe generalised elliptic-type integral Rμ(k, α, γ)where 0 ≤ k < 1, Re(γ) > Re(α) > 0, Re(μ) ≥ −0.5, is represented in terms of the Gauss hypergeometric function by Kalla, Conde and Hubbell [8]. In 1987, Kalla, Lubner and Hubbell derived a simple-structured single-term approximation for this function in the neighbourhood of k2 = 1 in some range of the parameters α, γ and μ. Another formula which complements the parameter range was recently derived by the author. In this paper a novel technique is used in deriving multiple-term efficient approximations (in the neighbourhood of k2 = 1) which may be considered as a generalisation to the concept of the single-term approximations mentioned above. Two non-overlapping expressions which almost cover the entire range of parameters (α, γ, μ) are derived. Closed-form solutions are obtained for single- and double-term approximations (in the neighbourhood of k2 = 1). Results show that the proposed technique is superior to existing approximations for the same number of terms. Our formulation has potential application for a wide class of special functions.

scholarly journals Closed-form error analysis of the non-identical Nakagami-m relay fading channel

2008 ◽  
Vol 12 (4) ◽  
pp. 259-261 ◽  
Author(s):  
H.A. Suraweera ◽  
G.K. Karagiannidis
Keyword(s):  
Error Analysis ◽  
Closed Form ◽  
Fading Channel ◽  
Form Error

A Novel Technique of Error Analysis Based on Test Case Combination

2014 ◽  
Vol 536-537 ◽  
pp. 255-258
Author(s):  
Xi Guo
Keyword(s):  
Error Analysis ◽  
Small Area ◽  
Fault Analysis ◽  
Test Case ◽  
Additional Test ◽  
System Parameters ◽  
Novel Technique ◽  
Software Debugging

Based on the model and feature of combination testing, a novel technique of fault analysis based on combination testing is proposed. The faults of software can be triggered by system parameters and their interaction. The result of combination testing is analyzed, and discovered the possible reasons, and then generates an additional test cased which involved from the test case causing the fault, and analysis and verify the result. This method can locate the faults in a relative small area, and can simplify the process of software debugging and testing.

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