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Date: 23-4-2019
4050
Date: 19-9-2018
1497
Date: 24-6-2019
1834
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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) |
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(4) |
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(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) |
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."
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