Numerically compute a function that is almost 1

Question

So my fellow numerical computational peeps it may be that I am suffering from sleep deprivation but I'm struggling to numerically compute a function x-> u(x) defined implicitly as follows:

 x^h(x) + x^-h(x) = a x

To be clear, that's just saying x raised to h(x) etc, and this should hold for all x. We can just consider x>0 and h(x)>0 actually.

May be a better question on [SciComp](http://scicomp.stackexchange.com/) , [Mathematics](http://math.stackexchange.com/) , or [MathOverflow](http://mathoverflow.net/) — Grice, Oct 21 '14 at 13:52

score 0 · Answer 1 · answered Oct 27 '14 at 14:23

0

I guess I'll leave the question here. The solution is to make the left hand side look like cosh(ax) and then we're done.

answered Oct 27 '14 at 14:23

Quant

4,253
3
17
15

Numerically compute a function that is almost 1

1 Answers1