[math-fun] Infinite product puzzle

21 Oct 2018

      A very nice identity for analytic functions is given by

(*)   π cot(π z)  =   lim   Sum_{-N <= n <= N} 1/(z-n)
                     N—>oo 

or briefly:

                    oo
               =  "Sum 1/(z-n)" 
                   -oo

The series (*) is convergent for each z in C - Z (the non-integral complex numbers)
(e.g., see https://people.reed.edu/~jerry/311/cotan.pdf).

Puzzle: 
-------
Determine which function is given by the corresponding infinite product
where it converges:

   f(z)  =   lim  Product_{-N <= n <= N}  (1 + 1/(z-n))
            N—>oo

—Dan

[math-fun] Infinite product puzzle

Dan Asimov