Re: [math-fun] Theta_3(0,q) near the unit circle

----- Original Message ---- From: "rwg@sdf.lonestar.org" <rwg@sdf.lonestar.org> To: math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, October 7, 2008 4:02:59 AM Subject: [math-fun] Theta_3(0,q) near the unit circle ... PS, how can a natural boundary grow only like 1/sqrt(-log q)? The other thetas are *much* wilder. _______________________________________________ Einar Hille gives the following example (Analytic Function Theory, vol. 1, p.133). sum( z^(2^n) / n!, n=0..infinity) This function and its derivatives of all orders are continuous and bounded in the closed unit disk. Yet the unit circle is a natural boundary. Gene