Erfi

Min Max

Min   Max       Re       Im

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)

REFERENCES:

Sloane, N. J. A. Sequences A000079/M1129, A001147/M3002, and A084253 in "The On-Line Encyclopedia of Integer Sequences."