08/16/2025, 04:36 PM
Welcome Pentalogue. I feel math and music are somewhat intimate fields, historically and conceptually.
If you want to understand EVERYTHING here then the best thing to do is to start from the Tetration FAQ and the wikipedia article on tetration.
After that there has been some progress with Trapmann and Kouznetsov theory of complex valued superfunctions, back in the days, and later, we discussed in details James Nixons's serie of papers about the application of his theory of infinite iterated composition and composition integrals to the problem of holomoprhic tetration and holomorphic (in the rank) hyperoperations.
Even more recently the user Natsugou made interesting contribution in the field of negative ranks hyperoperations by an interesting analysis of the algebraic phenomena behind recursion.
Feel free to ask more focused question creating new threads or writing on existing ones.
If you want to understand EVERYTHING here then the best thing to do is to start from the Tetration FAQ and the wikipedia article on tetration.
After that there has been some progress with Trapmann and Kouznetsov theory of complex valued superfunctions, back in the days, and later, we discussed in details James Nixons's serie of papers about the application of his theory of infinite iterated composition and composition integrals to the problem of holomoprhic tetration and holomorphic (in the rank) hyperoperations.
Even more recently the user Natsugou made interesting contribution in the field of negative ranks hyperoperations by an interesting analysis of the algebraic phenomena behind recursion.
Feel free to ask more focused question creating new threads or writing on existing ones.
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)