Talk:Entire function/Archive 1

Trigonometric and hyperbolic functions entire?
I'm not a mathematician, but how can it be true that the trigonometric and hyperbolic functions are entire? For example, the tangent function isn't even defined at π/2, so how can it be holomorphic there? —Caesura(t) 02:20, 1 March 2006 (UTC)
 * Whoever wrote that meant sine, cosine, sinh, and cosh, but I remved that thing altogether. Thanks. Oleg Alexandrov (talk) 03:08, 1 March 2006 (UTC)


 * I'm a layman, and have difficulties tying together the following two concepts:
 * Liouville's theorem which states that if an entire function f is bounded, then f is constant
 * Trigonometric functions like sine and cosine are entire.
 * Isn't sine a bounded entire function that is not constant, in contradiction to Liouville's theorem ? —Preceding unsigned comment added by 213.224.83.33 (talk) 17:54, 4 September 2008 (UTC)


 * You're thinking of real variables. While it is true that sinx is bounded for x real, this is no longer the case if x is complex.  Indeed, consider for instance
 * $$\sin(it) = \frac{e^{i(it)} - e^{-i(it)}}{2i} = \frac{e^{-t}-e^t}{2i}$$
 * which is unbounded. siℓℓy rabbit  (  talk  ) 19:22, 4 September 2008 (UTC)