11/11/26 09:46:58.28
>>764
１．Let ａ be an arbitrary real number and ｂ a positive real number. Evaluate the integral
∫[0,∞） cos(ax)/cosh(bx) dx.
（Recall that cosh(x) = (1/2)(e^x + e^-x) is the hyperbolic cosine.)
{Wed., 2010/Jan/20 (Day 2)}
２．Let ｆ be a holomorphic function on a domain containing the closed disc {z : |z|≦3}, and suppose that
f(1) = f(i) = f(-1) = f(-i) = 0.
Show that
|f(0)| ≦ (1/80)･max{|f(z)| : |z|=3},
and find all such functions for which equality holds in this inequality.
{Thu., 2010/Jan/21 (Day 3)}