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 Generalized arithmetic operator JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 03/11/2014, 03:15 PM (This post was last modified: 03/11/2014, 03:17 PM by JmsNxn.) Well I'm not certain, but your operators seem to be like a modified lower hyperoperators. These operators satisfy the recursion: $(x[s]y)[s-1] x = x[s](y+1)$ where $x[0]y = x+y$ Check if this function works. I'm pulling it out of a hat but I have a lot of math behind it.: $\frac{2}{x[s]y} = \frac{1}{\Gamma(-s)} \sum_{n=0}^\infty \frac{(-1)^n}{(x[n]y)n!(n-s)} + \sum_{k=0}^\infty \frac{a_k}{\Gamma(k-s+1)}$ where $a_k = \sum_{n=0}^\infty \frac{(-1)^k}{x[n+k]y}$ This may or may not work. Depending on if 1/x[s]y is holomorphic or meromorphic and if (x[s]y)[s-1]x is holo as well with decent enough behaviour. « Next Oldest | Next Newest »

 Messages In This Thread Generalized arithmetic operator - by hixidom - 03/11/2014, 03:52 AM RE: Generalized arithmetic operator - by JmsNxn - 03/11/2014, 03:15 PM RE: Generalized arithmetic operator - by hixidom - 03/11/2014, 06:24 PM RE: Generalized arithmetic operator - by MphLee - 03/11/2014, 10:49 PM RE: Generalized arithmetic operator - by hixidom - 03/11/2014, 11:20 PM RE: Generalized arithmetic operator - by MphLee - 03/12/2014, 11:18 AM RE: Generalized arithmetic operator - by JmsNxn - 03/12/2014, 02:59 AM RE: Generalized arithmetic operator - by hixidom - 03/12/2014, 04:37 AM RE: Generalized arithmetic operator - by MphLee - 03/12/2014, 06:19 PM RE: Generalized arithmetic operator - by hixidom - 03/12/2014, 06:43 PM RE: Generalized arithmetic operator - by tommy1729 - 03/21/2014, 10:31 PM RE: Generalized arithmetic operator - by hixidom - 03/22/2014, 12:06 AM RE: Generalized arithmetic operator - by tommy1729 - 03/22/2014, 12:13 AM RE: Generalized arithmetic operator - by hixidom - 03/22/2014, 12:42 AM RE: Generalized arithmetic operator - by hixidom - 06/11/2014, 05:10 PM

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