Steven Finch

collaborators

6 papers

math.NT2025

Half-Iterates and Delta Conjectures

Steven Finch

The vivid contrast between two competing algorithms for solving Abel's equation $g (I^¸ (x)) = g (x) + 1$ , given $I^¸ (x)$ , is easily sketched. EJ is faster and more efficient, but ML ev…

math.GM2025

Compositional Square Roots of $exp (x)$ and $1 + x^{2}$

Steven Finch

Our work began as an effort to understand calculations by Morris & Szekeres (1961) and Walker (1991) regarding fractional iteration.

math.NT2025

Exercises in Iterational Asymptotics III

Steven Finch

The nonlinear recurrences we consider here include simple continued fractions for the Golden & Silver means and a parametric family of cubics in connection with Abel's functional e…

math.NT2025

Exercises in Iterational Asymptotics II

Steven Finch

The nonlinear recurrences we consider here include the functions $3 x (1 - x)$ and $cos (x)$ , which possess attractive fixed points $2/3$ and $0.739...$ (Dottie's number). Detailed asy…

math.NT2025

Exercises in Iterational Asymptotics

Steven Finch

The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).

math.CA2024

What do sin $(x)$ and arcsinh $(x)$ have in Common?

Steven Finch

N. G. de Bruijn (1958) studied the asymptotic expansion of iterates of sin $(x)$ with $0 < x \leq I ¨ /2$ . Bencherif & Robin (1994) generalized this result to increasing analytic func…

Half-Iterates and Delta Conjectures

Compositional Square Roots of exp(x) and 1+x2

Exercises in Iterational Asymptotics III

Exercises in Iterational Asymptotics II

Exercises in Iterational Asymptotics

What do sin(x) and arcsinh(x) have in Common?

Compositional Square Roots of $exp (x)$ and $1 + x^{2}$

What do sin $(x)$ and arcsinh $(x)$ have in Common?