Furthermore, DLMF 7.17 only defines the inverse error function on the real
line (in fact (-1,1))
I do not recall ever seeing a discussion of the complex inverse error
function. Strecok (1968) shows that it satisfies y''=2yy'y',
but this is nonlinear, so the methodology of the paper below doesn't help.
Chyzak,F., Davenport,J.H., Koutschan,C. & Salvy,B.,
On Kahan's Rules for Determining Branch Cuts.
Proc. SYNSAC 2012 (ed. D. Wang et al.), IEEE Computer Society Press, Los
Alamitos, CA, pp. 47-51
On Friday, 27 December 2013 22:40:40 UTC, Buck Golemon wrote:
>
> 1) Sage seems unable to reduce `erf(x) == erf(y)` to `x == y`. How can I
> help this along?
>
> solve(erf(x) == erf(y), x)[0].simplify_full()
>
> Actual output: x == inverse_erf(erf(y))
> Expected output: x == y
>
> I had expected that sage would trivially reduce `inverse_erf(erf(y))` to
> `y`.
>
> 2) This output references 'inverse_erf', which doesn't seem to be
> importable t from anywhere in sage. Am I correct?
>
> ---
>
> My concrete problem is re-deriving the formula for the normal-distribution
> cdf. I get a good solution from sage, but fail in showing that it's
> equivalent to a known solution because:
>
> var('x sigma mu')
> assume(sigma > 0)
> eq3 = (-erf((sqrt(2)*mu - sqrt(2)*x)/(2*sigma)) == -erf((sqrt(2)*(mu -
> x))/(2*sigma)))
> bool(eq3)
>
> Actual output: False
> Expected output: True
>
>
> However this quite similar formula works fine:
>
> eq3 = (-erf(sqrt(2)*mu - sqrt(2)*x) == -erf(sqrt(2)*(mu - x)))
> bool(eq3)
>
> Output: True
>
> ---
> Include:
> Platform (CPU) -- x86_64
> Operating System -- Ubuntu 13.10
> Exact version of Sage (command: "version()") -- 'Sage Version 5.13,
> Release Date: 2013-12-15'
>
>
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