The generalized binomial coefficient for z in C (complex) and k = 0, 1, 2, ... is
1 if k = 0 and
( k )
( z ) = [z(z-1) ... (z - k +1)] / k!
if k >=1. For a fixed value of s in C we define the binomial series
B_s*(z) = sum of n=0, ^infinity, ( s )
( n ) z^n
See the formatted question attached.© BrainMass Inc. brainmass.com October 10, 2019, 5:26 am ad1c9bdddf
** Please see the attachment for the full solution with complete steps ** ...
In this solution, we show that the radius of convergence of the binomial series is 1 for all complex values of its argument.