Complex complementary error function

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1 total messages Started by Nico Temme Tue, 07 Apr 1992 08:23

#248

Author: Nico Temme
Date: Tue, 07 Apr 1992 08:23

26 lines
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> Hugh Songh writes:
> Has anybody tried to program this special function?  
> Can I convert the declaration statement of "fullerton's library"
> derfc appropriately to obtain the complex version?  BTW,
> fullerton's derfc seems to utilize Tchebyshev rational
> approximation.

Answer: no; you should never translate Tchebyshev rational
approximation for real intervals to the complex case.

>The other option is to implement Formula 7.1.29 of 
> Abramowitz/Stegun for complex erf, which is an 
> infinite series of a complex elementary functions.

Answer: formula 7.1.29 of Abramowitz/Stegun is quite 
acceptable. However, Algorithm 680 of TOMS (available through
netlib) is more efficient. It computes a 14d approximation 
of the function w(z) for complex values of z. See formula 7.1.3
 of Abramowitz/Stegun. A description of the algorithm is given in
TOMS, Vol. 16, pp.38-46, 1990.

-- 
Nico M. Temme                                   : nicot@cwi.nl
CWI (Centre for Mathematics & Computer Science) : tel +31 20 592 8020 x 35
Kruislaan 413, 1098 SJ Amsterdam, Netherlands.  : fax +31 20 592 4199
P.O. Box 4079, 1009 AB Amsterdam, Netherlands.

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