public static double s15af(
	double x
)

Public Shared Function s15af ( _
	x As Double _
) As Double

public:
static double s15af(
	double x
)

static member s15af : 
        x : float -> float 

s15af returns a value for Dawson's Integral, $F\left(x\right)$.

s15af evaluates an approximation for Dawson's Integral The method is based on two Chebyshev expansions:

For $0<\left|x\right|\le 4$, For $\left|x\right|>4$, For $\left|x\right|$ near zero, $F\left(x\right)\simeq x$, and for $\left|x\right|$ large, $F\left(x\right)\simeq \frac{1}{2x}$. These approximations are used for those values of $x$ for which the result is correct to machine precision.

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

None.

Let $\delta$ and $\epsilon$ be the relative errors in the argument and result respectively.

If $\delta$ is considerably greater than the machine precision (i.e., if $\delta$ is due to data errors etc.), then $\epsilon$ and $\delta$ are approximately related by: The following graph shows the behaviour of the error amplification factor $\left|\frac{x\left(1-2xF\left(x\right)\right)}{F\left(x\right)}\right|$:

However if $\delta$ is of the same order as machine precision, then rounding errors could make $\epsilon$ somewhat larger than the above relation indicates. In fact $\epsilon$ will be largely independent of $x$ or $\delta$, but will be of the order of a few times the machine precision.

None.

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This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.