Add description for ERF function.

docs/src/functions/engineering.md

@@ -27,7 +27,7 @@ All Engineering functions are already supported in IronCalc.
 | DEC2BIN      | <Badge type="tip" text="Available" /> | –             |
 | DEC2HEX      | <Badge type="tip" text="Available" /> | –             |
 | DEC2OCT      | <Badge type="tip" text="Available" /> | –             |
-| ERF          | <Badge type="tip" text="Available" /> | –             |
+| ERF          | <Badge type="tip" text="Available" /> | [ERF](engineering/erf) |
 | ERF.PRECISE  | <Badge type="tip" text="Available" /> | –             |
 | ERFC         | <Badge type="tip" text="Available" /> | –             |
 | ERFC.PRECISE | <Badge type="tip" text="Available" /> | –             |

docs/src/functions/engineering/erf.md

@@ -3,9 +3,49 @@ layout: doc
 outline: deep
 lang: en-US
 ---
-
-# ERF
-
+# ERF function
 ::: warning
-🚧 This function is implemented but currently lacks detailed documentation. For guidance, you may refer to the equivalent functionality in [Microsoft Excel documentation](https://support.microsoft.com/en-us/office/excel-functions-by-category-5f91f4e9-7b42-46d2-9bd1-63f26a86c0eb).
-:::
+**Note:** This draft page is under construction 🚧
+:::
+## Overview
+ERF (<u>ER</u>ror <u>Function</u>) 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(<span title="Number" style="color:#1E88E5">X</span>, <span title="Number" style="color:#1E88E5">Y</span>) => <span title="Number" style="color:#1E88E5">erf</span>**
+### Argument descriptions
+* *X* ([number](/features/value-types#numbers), required). Integration limit. If no value is supplied for the _Y_ argument, ERF integrates over the range [0, _X_].
+* *Y* ([number](/features/value-types#numbers), [optional](/features/optional-arguments)). 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](/features/value-types#numbers)  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!`](/features/error-types.md#error) error.
+* If the value of any argument is not (or cannot be converted to) a [number](/features/value-types#numbers), then ERF returns the [`#VALUE!`](/features/error-types.md#value) error.
+* For some argument values, ERF may return the [`#DIV/0!`](/features/error-types.md#div-0) error.
+
+<!--@include: ../markdown-snippets/error-type-details.txt-->
+## 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.
+<center><img src="/functions/images/error-function-curve.png" width="350" alt="Graph showing erf(x) for x between -3 and +3."></center>
+
+* This figure illustrates some of the key characteristics of the error function:
+
+  * erf($0$) = $0$
+  * erf($x$) = -erf($x$)
+  * As $x → ∞$, erf($x$) $→ 1$.
+  * As $x → -∞$, erf($x$) $→ -1$.
+
+* The error function is a [transcendental](https://en.wikipedia.org/wiki/Transcendental_function), non-algebraic mathematical function. IronCalc implements the ERF function by numerical approximation using a power series.
+## Examples
+[See some examples in IronCalc](https://app.ironcalc.com/?example=erf).
+
+## Links
+* See also IronCalc's [ERFC](/functions/engineering/erfc.md), [ERF.PRECISE](/functions/engineering/erf.precise.md) and [ERFC.PRECISE](/functions/engineering/ERFC.PRECISE.md) functions.
+* Visit Microsoft Excel's [ERF function](https://support.microsoft.com/en-gb/office/erf-function-c53c7e7b-5482-4b6c-883e-56df3c9af349) page.
+* Both [Google Sheets](https://support.google.com/docs/answer/9116267) and [LibreOffice Calc](https://wiki.documentfoundation.org/Documentation/Calc_Functions/ERF) provide versions of the ERF function.