Suppose f is entire and never vanishes and that none of the

Question

1. Show that if f is an entire function of finite order that omits two values, then f is constant. This result remains true for any entire function and is known as Picard's little theorem.

[Hint: If f misses a, then f(z) - a is of the form e^p(z) where p is a polynomial.]

2. Suppose f is entire and never vanishes, and that none of the higher derivatives of f ever vanish. Prove that if f is also of finite order, then f(z) = e^az+b for some constants a and b.