$\Delta y = e^{sy}$ or: How I Learned to Stop Worrying and Love the $\Gamma$-function
| Autor: | Nixon, James David |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a nice holomorphic function $f(s, z)$ in two variables, a respective holomorphic Gamma function $\Gamma = \Gamma_f$ is constructed, such that $f(s, \Gamma(s)) = \Gamma(s + 1)$. Along the way, we fall through a rabbit hole of infinite compositions, First Order Difference Equations, and absurd functional equations... This paper is orchestrated around an investigation into the unconventional equation $\Delta y = y(s+1)-y(s) = e^{sy(s)}$ and its solutions in the complex plane. Comment: 37 pages, 0 figures, 0 tables |
| Databáze: | arXiv |
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