Function Repository Resource:

# Erfci

Evaluate the integral of the complementary error function

Contributed by: Paco Jain (Wolfram Research)
 ResourceFunction["Erfci"][x] computes the definite integral of erfc(x).

## Details

Mathematical function, suitable for both symbolic and numerical manipulation.
The ResourceFunction["Erfci"] function is defined by the integral -Integrate[Erfc[t],{t,x,}]. In closed form, this is equivalent to -Exp[-x^2]/Sqrt[π] + x Erfc[x].
ResourceFunction["Erfci"] can be evaluated to arbitrary numerical precision.

## Examples

### Basic Examples (2)

Plot the Erfci function:

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Examine some particular values:

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### Scope (3)

Erfci can be applied to complex values:

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When applied to numerical values, Erfci reflects the precision of its input:

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### Applications (1)

Plot Erfci over a subset of the complexes:

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## Requirements

Wolfram Language 11.3 (March 2018) or above

## Version History

• 1.0.1 – 14 September 2021
• 1.0.0 – 27 February 2019