On Sat, Apr 5, 2008 at 6:39 PM, Ryan James <[EMAIL PROTECTED]> wrote: > > On Sat, 2008-04-05 at 18:25 +0200, Ondrej Certik wrote: > > > BTW - is there any application, where you actually get one > > trigonometric function in the other: > > > > sin(cos(x)) > > > > ? > > the integral forms of bessel functions of the first and second kind > contain integral(cos(z*sin(t) - v*t), (t, 0, pi)), but that's the only > place i recall seeing them.
You are right - whenever there is exp(z) and we are integrating it over some circle z = exp(i*phi), which is a very common operation, you get the nested trigonometric functions: exp(z) = exp(exp(i*phi)) = exp(cos(phi)) * (cos(sin(phi)) + i * sin(sin(phi))) Interesting. On Mon, Apr 7, 2008 at 10:12 PM, Saroj Adhikari <[EMAIL PROTECTED]> wrote: > > Thanks Ryan for the information. > > It is equivalent to the real part of > ⌠ > ⎮ 1 > ⎮ ─ > ⎮ n z > ⎮ z *ℯ dz > ⌡ > > over a unit circle (exp(iθ). The answer simplifies to (2*π)/n!) Thanks for the hint, now it should be easy. I'll try to fill in the missing steps, when I get bored. :) > Ondrej, I wish I could send integral patches for these complicated > integrals.. :) Ondrej --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---
