Generalized elementary functions. (English) Zbl 1520.30056

Kiselman, Christer Oscar

Complex Var. Elliptic Equ. 68, No. 6, 918-931 (2023).

Summary: Ramon Edgar Moore and Alexander M. Gofen introduced a generalization of Joseph Liouville’s concept of elementary functions. Gofen even defined two variants of these, viz. scalar generalized elementary functions and vector generalized elementary functions, and formulated a conjecture concerning them. We prove that, for some modified conjectures, the two classes are different.

MSC:

30E99	Miscellaneous topics of analysis in the complex plane
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

ordinary differential equations; elementary functions; generalized elementary functions

References:

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