Leah-Cosine and -Sine Functions: Definitions and Elementary Properties
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Abstract
The two standard sets of periodic special functions are the trigonometric cosine and sine, and the Jacobi cosine and sine functions. Both sets may be defined as solutions to initial-value problems involving, respectively, linear and nonlinear, second-order, ordinary differential equations. We show that it is possible to extend these classes of functions to a new set of special functions, which are called (by Mickens) the Leah-cosine and Leah-sine. The main purpose of this chapter is to provide definitions of these functions and derive some of their more important mathematical properties.
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