The "imaginary error function" is an entire function
defined by
|
(1)
|
where is the erf
function. It is implemented in the Wolfram
Language as Erfi[z].
has derivative
|
(2)
|
and integral
|
(3)
|
It has series about
given by
|
(4)
|
(where the terms are OEIS A084253), and series
about infinity given by
|
(5)
|
(OEIS A001147 and A000079).
See also
Dawson's Integral,
Erf,
Erfc
Related Wolfram sites
http://functions.wolfram.com/GammaBetaErf/Erfi/
Explore with Wolfram|Alpha
References
Sloane, N. J. A. Sequences A000079/M1129, A001147/M3002, and A084253
in "The On-Line Encyclopedia of Integer Sequences."Referenced
on Wolfram|Alpha
Erfi
Cite this as:
Weisstein, Eric W. "Erfi." From MathWorld--A
Wolfram Web Resource. https://mathworld.wolfram.com/Erfi.html
Subject classifications