erf_realreturns the value of the error function .
For full information please refer to the NAG Library document for s15ae
The argument of the function.
The value of the error function .
erf_realcalculates an approximate value for the error function
Let be the root of the equation (then ). For the value of is based on the following rational Chebyshev expansion for :
where denotes a rational function of degree in the numerator and in the denominator.
For the value of is based on a rational Chebyshev expansion for : for the value is based on the expansion
and for it is based on the expansion
For each expansion, the specific values of and are selected to be minimal such that the maximum relative error in the expansion is of the order , where is the maximum number of decimal digits that can be accurately represented for the particular implementation (see
For there is a danger of setting underflow in . For ,
erf_realreturns ; for it returns .
NIST Digital Library of Mathematical Functions
Cody, W J, 1969, Rational Chebyshev approximations for the error function, Math.Comp. (23), 631–637