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 product functions tommy1729 Ultimate Fellow Posts: 1,358 Threads: 330 Joined: Feb 2009 05/31/2011, 11:00 PM yeah , i was somewhat aware of all that. more specifically a theorem by hadamard or was it weierstrass : any entire function can be written as f(z) = exp(taylor(z)) * (z - a_1)(z - a_2)..(z - a_n)... i guess this implies if f(z)/f(0) is entire then f(z)/f(0) = 1 + a_1 z + a_2 z^2 + ... = (1 + b_1 z)(1 + b_2 z^2) ... and the product form also converges for all z apart from the set of points (-1/b_n)^(1/n) (unless they truely give 0 ) IFF those zero's are nowhere dense ( so that they do not form a " natural boundary " if there are oo many zero's ). to avoid bounded non-cauchy sequences , i do assume a simple summability method is used ( averaging ). ( or "productability method " -> exp ( summability ( sum log (c_n) ) ) ) tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread product functions - by tommy1729 - 05/31/2011, 12:26 PM RE: product functions - by bo198214 - 05/31/2011, 02:02 PM RE: product functions - by bo198214 - 05/31/2011, 02:13 PM RE: product functions - by tommy1729 - 05/31/2011, 11:00 PM RE: product functions - by tommy1729 - 06/01/2011, 05:31 PM RE: product functions - by tommy1729 - 06/01/2011, 05:38 PM

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