Exercise 15.  Explain why the composition of two entire functions is an entire function.  

Solution 15.

See text and/or instructor's solution manual.

Solution.  Given that  f(z)  and  g(z)  are entire functions, then  f'(z)  and  g'(z)  exist for all  z.

Then the composition     is entire because      exists for all  z.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell