Experimental Mathematics

Abel's equation and regular growth: variations on a theme by Abel

George Szekeres

Abstract

Following a 70-year old suggestion of Paul Lévy, a condition is formulated for the regularity of growth of real functions. The condition, which is quite explicit, makes use of the iterates of the function and solutions of Abel's functional equation, and is well adapted to a computer testing.

Numerous computer experiments reveal interesting properties of the proposed regularity criterion.

Article information

Source
Experiment. Math. Volume 7, Issue 2 (1998), 85-100.

Dates
First available in Project Euclid: 24 March 2003

Permanent link to this document
http://projecteuclid.org/euclid.em/1048515657

Mathematical Reviews number (MathSciNet)
MR1677107

Zentralblatt MATH identifier
0918.39006

Subjects
Primary: 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]
Secondary: 39B22: Equations for real functions [See also 26A51, 26B25]

Citation

Szekeres, George. Abel's equation and regular growth: variations on a theme by Abel. Experiment. Math. 7 (1998), no. 2, 85--100. http://projecteuclid.org/euclid.em/1048515657.


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