naginterfaces.library.specfun.erfc_​complex

naginterfaces.library.specfun.erfc_complex(z)[source]

erfc_complex computes values of the function , for complex .

For full information please refer to the NAG Library document for s15dd

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s15ddf.html

Parameters
zcomplex

The argument of the function.

Returns
erfczcomplex

The value of the function evaluated at , .

Raises
NagValueError
(errno )

Result has no precision when entered with argument .

Warns
NagAlgorithmicWarning
(errno )

Real part of result overflows when entered with argument .

(errno )

Imaginary part of result overflows when entered with argument .

(errno )

Both real and imaginary parts of result overflow when entered with argument .

(errno )

Result has less than half precision when entered with argument .

Notes

erfc_complex computes values of the function , where is the complementary error function

for complex . The method used is that in Gautschi (1970) for in the first quadrant of the complex plane, and is extended for in other quadrants via the relations and . Following advice in Gautschi (1970) and van der Laan and Temme (1984), the code in Gautschi (1969) has been adapted to work in various precisions up to decimal places. The real part of is sometimes known as the Voigt function.

References

Gautschi, W, 1969, Algorithm 363: Complex error function, Comm. ACM (12), 635

Gautschi, W, 1970, Efficient computation of the complex error function, SIAM J. Numer. Anal. (7), 187–198

van der Laan, C G and Temme, N M, 1984, Calculation of special functions: the gamma function, the exponential integrals and error-like functions, CWI Tract 10, Centre for Mathematics and Computer Science, Amsterdam