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 A support for Andy's (P.Walker's) slog-matrix-method JmsNxn Long Time Fellow Posts: 571 Threads: 95 Joined: Dec 2010 03/08/2021, 07:13 PM (This post was last modified: 03/08/2021, 07:25 PM by JmsNxn.) Actually the paper isn't as bad as I remember, lol. Here's a link: https://arxiv.org/pdf/1503.06211.pdf I do take for granted that the reader knows what Ramanujan's Master Theorem is. The version I use is, if, $ |f(z)| \le C e^{\alpha |\Im(z)| + \rho|\Re(z)|}\,\,\alpha < \pi/2,\,\,C,\rho > 0\\ f\,\,\text{is holomorphic for}\,\,\Re(z) > 0\\ \text{Then f can be represented as}\\ \Gamma(1-z)f(z) = \sum_{n=0}^\infty f(n+1)\frac{(-1)^n}{n!(n+1-z)} + \int_1^\infty (\sum_{n=0}^\infty f(n+1)\frac{(-x)^n}{n!})x^{-z}\,dx\\$ Which is nothing more than a slightly tweaked version of Ramanujan's Master Theorem. I choose to write this using fractional calculus, where if, $ \vartheta(x) = \sum_{n=0}^\infty f(n+1) \frac{x^n}{n!}\\ f(z) = \frac{d^{z-1}}{dx^{z-1}}|_{x=0} \vartheta(x)\\$ « Next Oldest | Next Newest »

 Messages In This Thread A support for Andy's (P.Walker's) slog-matrix-method - by Gottfried - 11/14/2011, 04:01 AM RE: A support for Andy's (P.Walker's) slog-matrix-method - by JmsNxn - 03/07/2021, 08:21 PM RE: A support for Andy's (P.Walker's) slog-matrix-method - by Gottfried - 03/07/2021, 10:14 PM RE: A support for Andy's (P.Walker's) slog-matrix-method - by tommy1729 - 03/07/2021, 10:37 PM RE: A support for Andy's (P.Walker's) slog-matrix-method - by JmsNxn - 03/08/2021, 07:13 PM

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