Re: Inverting Sin(x)=x

From: David W. Cantrell (DWCantrell_at_sigmaxi.org)
Date: 07/29/04 

Date: 29 Jul 2004 19:07:44 GMT

John Schutkeker <johnny--mander@sbcglobal.net-nospam> wrote:
> David W. Cantrell <DWCantrell@sigmaxi.org> wrote in
> news:20040728103805.042$xY@newsreader.com:
[snip]
> What I'm wondering about is inverting y=Sin(x)+x. Given y(x), solve
> for x(y). Is this not an inverse?

Yes, it is.

> I've found a fair amount about series solutions, but they're not strictly
> closed form. That's what I'm asking about.

And of course, there's much about series solutions in the Colwell reference
I'd mentioned earlier. But they're attempting to solve Kepler's equation in
general. If you want to solve specifically just y=Sin(x)+x, then there are
series solutions which are perhaps unknown to you. For example, see the
last two articles in <http://mathforum.org/discuss/sci.math/t/360856>.

There is no closed-form solution in terms of familiar functions. However,
closed-form approximations could be certainly devised.

David Cantrell