demoivre and hyperbolic functions
- Subject: demoivre and hyperbolic functions
- From: Barton Willis
- Date: Sun, 11 Apr 2010 12:37:08 -0500
Try something like this:
(%i11) mydemoivre(e) := subst("^" = lambda([a,b], if a = %e then cosh(b) + sinh(b) else a^b),demoivre(e))$
(%i12) exponentialize(cosh(x));
(%o12) (%e^x+%e^(-x))/2
(%i13) mydemoivre(%);
(%o13) cosh(x)
(%i16) exponentialize(cosh(x) = 6 * sinh(z)/z);
(%o16) (%e^x+%e^(-x))/2=(3*(%e^z-%e^(-z)))/z
(%i17) mydemoivre(%);
(%o17) cosh(x)=(6*sinh(z))/z
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>This?works?fine:
>
>(%i10)?exponentialize(cos(x));
>(%o10)?(%e^(%i*x)+%e^-(%i*x))/2
>
>(%i11)?demoivre(%);
>(%o11)?cos(x)
>
>but?this?does?not:
>
>(%i12)?exponentialize(cosh(x));
>(%o12)?(%e^x+%e^-x)/2
>
>(%i13)?demoivre(%);
>(%o13)?(%e^x+%e^-x)/2
>
>Is?there?a?function?that?can?do?what?demoivre?does
>for?trigonometric?function?
>
>
>--?Raoul
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