Solutions of the equation $a_n + (a_{n-1} + \cdots (a_2 + (a_1 + x^{r_1})^{r_2}\cdots )^{r_{n}} = b\, x$

Daniel Panazzolo

paper

Solutions of the equation $a_{n} + (a_{n - 1} + \dots (a_{2} + (a_{1} + x^{r_{1}})^{r_{2}} \dots)^{r_{n}} = b x$

arXiv:2405.03179

Abstract

We establish a novel upper bound for the real solutions of the equation specified in the title, employing a generalized derivation-division algorithm. As a consequence, we also derive a new set of Chebyshev functions adapted specifically for this problem.

Solutions of the equation an​+(an−1​+⋯(a2​+(a1​+xr1​)r2​⋯)rn​=bx

Abstract

Solutions of the equation $a_{n} + (a_{n - 1} + \dots (a_{2} + (a_{1} + x^{r_{1}})^{r_{2}} \dots)^{r_{n}} = b x$