Inverse Erfc

The inverse erf function is the inverse function  of  such that

(1)

with the first identity holding for  and the second for . It is implemented in the Wolfram Language as InverseErfc[z].

It is related to inverse erf by

(2)

It has the special values

			(3)
			(4)
			(5)

It has the derivative

(6)

and its indefinite integral is

(7)

(which follows from the method of Parker 1955).

The Taylor series about 1 is given by

(8)

(OEIS A002067 and A007019).

REFERENCES:

Bergeron, F.; Labelle, G.; and Leroux, P. Ch. 5 in Combinatorial Species and Tree-Like Structures. Cambridge, England: Cambridge University Press, 1998.

Carlitz, L. "The Inverse of the Error Function." Pacific J. Math. 13, 459-470, 1963.

Parker, F. D. "Integrals of Inverse Functions." Amer. Math. Monthly 62, 439-440, 1955.

Sloane, N. J. A. Sequences A002067/M4458, A007019/M3126, A092676, and A092677 in "The On-Line Encyclopedia of Integer Sequences."