Basic |
Computes log(1 + z) with relative error accuracy near z = 0.
Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3572.0 (4.8.3572.0)
SyntaxC#
public static Complex LogRel( Complex z )
Parameters
- z Complex
- The complex argument z.
Return Value
Complexlog(1 + z) computed with improved relative accuracy for values of z near 0.
Remarks
April 1977 version. W. Fullerton, c3, Los Alamos Scientific Lab.
let rho = abs(z) and
r**2 = abs(1+z)**2 = (1+x)**2 + y**2 = 1 + 2*x + rho**2 .
now if rho is small we may evaluate LogRel(z) accurately by
log(1+z) = complex (log(r), arg(1+z))
= complex (0.5*log(r**2), arg(1+z))
= complex (0.5*LogRel(2*x+rho**2), arg(1+z))
See Also