ERF function

Note: This draft page is under construction 🚧

Overview

ERF (ERror Function) is a function of the Engineering category that calculates a value for the error function. Also known as the Gauss error function, the error function represents the probability of a random variable falling within a certain range, given that it follows a specified normal distribution.

Usage

Syntax

ERF(X, Y) => erf

Argument descriptions

• X (number, required). Integration limit. If no value is supplied for the Y argument, ERF integrates over the range [0, X].
• Y (number, optional). Upper integration limit. When a value is supplied for this argument, ERF integrates over the range [X, Y].

Additional guidance

None.

Returned value

ERF returns a number that is the error function probability for the specified arguments. The returned value has a magnitude in the range [0, 1] but may be either positive (upper integration limit > lower integration limit) or negative (upper integration limit < lower integration limit).

Error conditions

• In common with many other IronCalc functions, ERF propagates errors that are found in its arguments.

• If no argument, or more than two arguments, are supplied, then ERF returns the #ERROR! error.

• If the value of any argument is not (or cannot be converted to) a number, then ERF returns the #VALUE! error.

• For some argument values, ERF may return the #DIV/0! error.

• For more information about the different types of errors that you may encounter when using IronCalc functions, visit our Error Types page.

Details

• The error function arises in many scientific, engineering, and mathematical fields and is commonly defined by the following equation (applicable for any real number $x$):

$$\text{erf}(x)=\frac{2}{\sqrt{\pi }}{\int }_0^x{e}^{-t^2}dt$$

• The figure below illustrates the output of the ERF function for values of $x$ in the range -3 to +3.

• This figure illustrates some of the key characteristics of the error function:

  • $\text{erf}(0)=0$
  • $\text{erf}(x)=-\text{erf}(x)$
  • As $x\to \mathrm{\infty }$, $\text{erf}(x)\to 1$
  • As $x\to -\mathrm{\infty }$, $\text{erf}(x)\to -1$

• The error function is a transcendental, non-algebraic mathematical function. IronCalc implements the ERF function by numerical approximation using a power series.

Examples

See some examples in IronCalc.

Links

• See also IronCalc's ERFC, ERF.PRECISE and ERFC.PRECISE functions.
• Visit Microsoft Excel's ERF function page.
• Both Google Sheets and LibreOffice Calc provide versions of the ERF function.