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 product functions tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 06/01/2011, 05:31 PM (This post was last modified: 06/01/2011, 05:31 PM by tommy1729.) i have to add some conditions and ideas : if f(z) = f(g(z)) then we have product terms of the form 1 + b_n g(z)^n. those product terms have different zero's despite f(z) = f(g(z)). also it seems if f ' (z) = 0 our product form does not work. so i propose the following condition. the product form of f(z) converges to the correct value in Q if f(z) =/= 0 and f(z) is univalent in Q. *** it would be nice to consider product forms of f^[n](z). $f^n(z)=z+\frac{1}{2} n z^2 + \frac{1}{12} (3n^2-n) z^3 + \frac{1}{48} (6n^3-5n^2+n) z^4 + \cdots$ is the expression for f(z) = e^z - 1 and it would be nice to have a similar looking product form ... « 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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