## Analyticity and Function Satisfying :$\displaystyle \ F'=e^{{f}^{-1}}$

**Authors:** Zeraoulia Rafik

In this note we present some new results about the analyticity of the functional-differential equation $ f'=e^{{f}^{-1}}$ at $ 0$ with $f^{-1}$ is a compositional inverse of $f$ , and the growth rate of $f_-(x)$ and $f_+(x)$ as $x\to \infty$ , and we will check the analyticity of some functional equations which they were studied before and had a relashionship with the titled functional-differential and we will conclude our work with a conjecture related to Borel- summability and some interesting applications of some divergents generating function with radius of convergent equal $0$ in number theory

**Comments:** 23 Pages. I wish my results w'd be considerable for any futur refeered journal

**Download:** **PDF**

### Submission history

[v1] 2018-02-10 14:44:28

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