erfcx

Scaled complementary error function

📝Syntax

R = erfcx(X)

📥Input Arguments

Parameter	Description
X	a real single or real double scalar, vector, matrix, or multidimensional array. Sparse and complex inputs are not supported.

📤Output Arguments

Parameter	Description
R	scaled complementary error function values, returned with the same size and floating-point class as X.

📄Description

erfcx computes the scaled complementary error function element by element.

The scaled complementary error function is defined as:

$$erfcx(x) = e^{x^2} erfc(x)$$

Use erfcx instead of exp(x^2) * erfc(x) for large positive X to avoid underflow, overflow, or loss of accuracy.

For large positive X:

$$erfcx(x) \approx \frac{1}{\sqrt{\pi}x}$$

💡Examples

Find the scaled complementary error function of a scalar.

R = erfcx(5)

Find the scaled complementary error function of the elements of a vector.

V = [-Inf -1 0 1 10 Inf];
R = erfcx(V)

Find the scaled complementary error function of the elements of a matrix.

M = [-0.5 15; 3.2 1];
R = erfcx(M)

Avoid overflow in exp(x^2) * erfc(x).

x = 35;
A = exp(x^2) * erfc(x);
B = erfcx(x);

🔗See Also

🕔Version History

Version	Description
1.17.0	initial version