ERF Function

Description

The ERF function computes the Gauss error function value. The mathematical definition of the Gauss error function is:

erf(x) = (2/√π) ∫₀ˣ e(-t²) dt

This function is widely used in probability theory, statistics, and partial differential equations, commonly employed to describe the cumulative distribution function of the normal distribution.

Syntax

erf(expr)

Parameters

• expr: A numeric expression for which to compute the error function value. Supports numeric types (implicitly castable to DOUBLE).

Returns

The return type is DOUBLE, representing the error function value corresponding to the input. The return value range is [-1, 1].

Examples

1. Compute erf(0):

   SELECT erf(0) AS res;
   +-----+
   | res |
   +-----+
   | 0   |
   +-----+
   

2. Compute erf(1):

   SELECT erf(1) AS res;
   +--------------------+
   |        res         |
   +--------------------+
   | 0.8427007929497149 |
   +--------------------+
   

3. Compute the error function value for a negative number (erf is an odd function, erf(-x) = -erf(x)):

   SELECT erf(-1) AS res;
   +---------------------+
   |         res         |
   +---------------------+
   | -0.8427007929497149 |
   +---------------------+
   

4. When the input is NULL:

   SELECT erf(NULL) AS res;
   +------+
   | res  |
   +------+
   | NULL |
   +------+
   

Notes

• When the input parameter is NULL, the result is NULL.
• The return value range of erf is [-1, 1]. As x → +∞, erf(x) → 1; as x → -∞, erf(x) → -1.
• erf is an odd function, i.e., erf(-x) = -erf(x), and erf(0) = 0.
• This function is often used in conjunction with normal distribution calculations, e.g., the cumulative distribution function of the standard normal distribution Φ(x) = (1 + erf(x/√2)) / 2.