This converges nowhere. The sum of a series can only converge if the limit of th summands is 0. Here it's 2, for any nonintegral z, and for integral z it's not even defined. ---------- Forwarded message --------- From: Dan Asimov <dasimov@earthlink.net> Date: Sun, Oct 21, 2018, 22:51 Subject: [math-fun] Infinite product puzzle To: <math-fun@mailman.xmission.com> 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 mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun