Editing Error function (section)

==Name==
The name "error function" and its abbreviation {{math|erf}} were proposed by [[James Whitbread Lee Glaisher|J. W. L. Glaisher]] in 1871 on account of its connection with "the theory of Probability, and notably the theory of [[errors and residuals|Errors]]."<ref name="Glaisher1871a">{{cite journal|last1=Glaisher|first1=James Whitbread Lee|title= On a class of definite integrals|journal=London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|date=July 1871 |volume=42 |pages=294–302|access-date=6 December 2017|url=https://books.google.com/books?id=8Po7AQAAMAAJ&pg=RA1-PA294 |number=277 |series=4 |doi=10.1080/14786447108640568}}</ref> The error function complement was also discussed by Glaisher in a separate publication in the same year.<ref name="Glaisher1871b">{{cite journal|last1=Glaisher|first1=James Whitbread Lee|title=On a class of definite integrals. Part II|journal=London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science|date=September 1871 |volume=42|pages=421–436|access-date=6 December 2017|url=https://books.google.com/books?id=yJ1YAAAAcAAJ&pg=PA421 |series=4 |number=279 |doi=10.1080/14786447108640600}}</ref>
For the "law of facility" of errors whose [[probability density|density]] is given by
<math display="block">f(x) = \left(\frac{c}{\pi}\right)^{1/2} e^{-c x^2}</math>
(the [[normal distribution]]), Glaisher calculates the probability of an error lying between {{mvar|p}} and {{mvar|q}} as:
<math display="block">\left(\frac{c}{\pi}\right)^\frac{1}{2} \int_p^qe^{-cx^2}\,\mathrm dx = \tfrac{1}{2}\left(\operatorname{erf} \left(q\sqrt{c}\right) -\operatorname{erf} \left(p\sqrt{c}\right)\right).</math>
[[File:Plot of the error function Erf(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg|alt=Plot of the error function Erf(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D|thumb|Plot of the error function Erf(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D]]