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 Does the Mellin transform have a half-iterate ? JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 05/07/2014, 03:22 PM Well I posted a reply to this but it deleted it :/ I have looked at this for so long Tommy. It's very closely related to tetration. I'll tell you how I can do it for some functions. $M(f) = \int_0^\infty f(x)x^{s-1}\,dx$ define $\vartheta(w) = \sum_{n=0}^\infty M^n(f)(s) \frac{w^n}{n!}$ Then if $\phi(z) = [\frac{d^z}{dw^z} \vartheta(w)]_{w=0}$ then $\phi(z) = M^z (f)(s)$ However we have to show lots of conditions on convergence and what not. « Next Oldest | Next Newest »

 Messages In This Thread Does the Mellin transform have a half-iterate ? - by tommy1729 - 05/06/2014, 10:25 PM RE: Does the Mellin transform have a half-iterate ? - by JmsNxn - 05/07/2014, 03:22 PM RE: Does the Mellin transform have a half-iterate ? - by tommy1729 - 05/07/2014, 11:17 PM RE: Does the Mellin transform have a half-iterate ? - by tommy1729 - 05/07/2014, 11:42 PM RE: Does the Mellin transform have a half-iterate ? - by tommy1729 - 05/07/2014, 11:52 PM

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