Superexponentials: A Generalization of Hyperbolic and Trigonometric Functions

  • Alfonso F. Agnew Department of Mathematics, Gravitational Wave Physics and Astronomy Center California State University, Fullerton, Fullerton, CA 92834
  • Brandon Gentile Department of Mathematics, California State University, Fullerton, Fullerton, CA 92834
  • John H. Mathews Department of Mathematics, California State University, Fullerton, Fullerton, CA 92834
DOI: https://doi.org/10.14505//jmef.v3.1(4).01

Abstract

We construct and explore the properties of a generalization of hy- perbolic and trigonometric functions we cal l superexponentials. The general ization is based on the characteristic second-order differential equations (DE) these functions satisfy, and leads to functions satisfying analogous mth order equations and having many properties analogous to the usual hyperbolic and trigonometric functions. Roots of unity play a key role in providing the periodicity resulting in various properties. We also show how these functions solve the general initial value problem for the differential equations y(n) = y, and a look at the power series expansions reveal surprisingly simple patterns that clarify the properties of the superexponentials.

References

Ahlfors, L. (1979). Complex Analysis. 3rd ed., McGraw-Hill, NewYork, N.Y.
Dummitand, D.S. and R. M. Foote (1991). Abstract Algebra. Prentice-Hall, Englewood Cliffs, NJ.
Published
2017-08-25
How to Cite
AGNEW, Alfonso F.; GENTILE, Brandon; MATHEWS, John H.. Superexponentials: A Generalization of Hyperbolic and Trigonometric Functions. Journal of Mathematical Economics and Finance, [S.l.], v. 3, n. 1, p. 7 - 22, aug. 2017. ISSN 2458-0813. Available at: <https://journals.aserspublishing.eu/jmef/article/view/1353>. Date accessed: 23 apr. 2024. doi: https://doi.org/10.14505//jmef.v3.1(4).01.
Citation Formats
Issue
Vol 3 No 1 (2017): JMEF Volume III, Issue 1(4), Summer 2017
Section
Articles

The Copyright Transfer Form to ASERS Publishing (The Publisher)
This form refers to the manuscript, which an author(s) was accepted for publication and was signed by all the authors.
The undersigned Author(s) of the above-mentioned Paper here transfer any and all copyright-rights in and to The Paper to The Publisher. The Author(s) warrants that The Paper is based on their original work and that the undersigned has the power and authority to make and execute this assignment. It is the author's responsibility to obtain written permission to quote material that has been previously published in any form. The Publisher recognizes the retained rights noted below and grants to the above authors and employers for whom the work performed royalty-free permission to reuse their materials below. Authors may reuse all or portions of the above Paper in other works, excepting the publication of the paper in the same form. Authors may reproduce or authorize others to reproduce the above Paper for the Author's personal use or for internal company use, provided that the source and The Publisher copyright notice are mentioned, that the copies are not used in any way that implies The Publisher endorsement of a product or service of an employer, and that the copies are not offered for sale as such. Authors are permitted to grant third party requests for reprinting, republishing or other types of reuse. The Authors may make limited distribution of all or portions of the above Paper prior to publication if they inform The Publisher of the nature and extent of such limited distribution prior there to. Authors retain all proprietary rights in any process, procedure, or article of manufacture described in The Paper. This agreement becomes null and void if and only if the above paper is not accepted and published by The Publisher, or is with drawn by the author(s) before acceptance by the Publisher.