Show that for ,
Here is my solution : consider the function . Its zeroes are and for , Thus its zeroes are all , , which are the zeroes of .
Moreover we know must be an entire function because it is a product of entire functions. By the identity theorem for entire functions, we must have for some . If we consider the coefficient of in the series expansion of about , we see that it is equal to , and on the left side as well. Hence we must have and .