# ERFC.1 Introduction

Let be a complex variable of .The function Complementary Error Function (noted ) is defined by the following second order differential equation

ERFC.1.1

The initial conditions of ERFC.1.1 are given at by

 ERFC.1.2

Related function: Error Function

# ERFC.2 Series and asymptotic expansions

## ERFC.2.1 Taylor expansion at

ERFC.2.1.1.1

### ERFC.2.1.2 General form

top up back next into bottom

 ERFC.2.1.2.1
The coefficients satisfy the recurrence
ERFC.2.1.2.2
Initial conditions of ERFC.2.1.2.2 are given by
ERFC.2.1.2.3

## ERFC.2.2 Asymptotic expansion at

### ERFC.2.2.1 First terms

top up back next into bottom

where

### ERFC.2.2.2 General form

#### ERFC.2.2.2.1 Auxiliary function

The coefficients of satisfy the following recurrence whose initial conditions are given by This recurrence has the closed form solution

# ERFC.3 Graphs

## ERFC.3.1 Real axis

top up back next into bottom

## ERFC.3.2 Complex plane

top up back next into bottom

 This web site is compliant with HTML 4.01 and CSS 1. Copyright © 2001-2003 by the Algorithms Project and INRIA. All rights reserved. Created: Aug 1 2003 15:11:38.