[Maxima] Feature request: cosh(asinh(x)) = sqrt(x^2+1)
Raymond Toy (RT/EUS)
raymond.toy at ericsson.com
Tue Jan 22 11:29:30 CST 2008
Stavros Macrakis wrote:
> On Jan 22, 2008 10:08 AM, Raymond Toy (RT/EUS) <raymond.toy at ericsson.com
> <mailto:raymond.toy at ericsson.com>> wrote:
> >> cosh(asinh(x)) = sqrt(x^2 + 1)
> Should maxima already know this and if so, how
> should it be done? I think it would be easy to add this rule in
> trigo.lisp, but is that the right thing to do?
> Sure, why not? And the simplification should respect triginverses. I'm
Mostly because rules are relatively simple to explain to people. But I
know lisp better than maxima, so for me, changing trigo is easier. :-)
> assuming no one wants the written-out forms of asinh(cosh(x)),
> atan(sinh(x)), etc. to be built-in, though. They are rather messy and
> you might as well use logarc/exponentialize.
I was only thinking about cosh(asinh(x)) and sinh(acosh(x)). Maybe a
few others. I'm not sure that sinh(acosh(x)) has the right branch cuts.
When I apply exponentialize, logarc, and ratsimp, I get
sqrt(x-1)*sqrt(x+1). I'll have to think about whether this result is
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