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Function Repository Resource:

Erfci

Source Notebook

Set up a symbol to give an error message when called with an unexpected number of arguments

Contributed by: Paco Jain (Wolfram Research)

ResourceFunction["Erfci"][x]

computes the definite integral of Erfc[x].

Details and Options

Mathematical function, suitable for both symbolic and numerical manipulation.
The ResourceFunction["Erfci"] function is defined through Integrate[Erfc[t],{t,0,x}]+C, where C=-1/Sqrt[π] is an integration constant. In closed form this is equivalent to Exp[-x^2]/Sqrt[π] + x Erfc[x].
ResourceFunction["Erfci"] has the attributes Listable and NumericFunction.
ResourceFunction["Erfci"] can be evaluated to arbitrary numerical precision.

Examples

Basic Examples

Plot the Erfci function:

In[1]:=
Plot[ResourceFunction["Erfci"][x], {x, -2, 2}]
Out[1]=

Examine some particular values:

In[2]:=
ResourceFunction["Erfci"][0]
Out[2]=
In[3]:=
ResourceFunction["Erfci"][2]
Out[3]=

Scope

Erfc can be applied to complex values:

In[4]:=
ResourceFunction["Erfci"][2 + 3 I ]
Out[4]=
In[5]:=
% // N
Out[5]=

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

In[6]:=
ResourceFunction["Erfci"][N[Pi, 100]]
Out[6]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

License Information