On Dixon elliptic functions and their Sumudu transforms : Connections to associated continued fractions expansions and Hankel determinants

Abstract

In this research work, Dixon elliptic functions having modulus $\alpha = 0$ for higher arbitrary powers, are treated with the Sumudu transform. From the resulting three term recurrences, product of the associated continued fractions expansions are given.  Then, corresponding Hankel determinants are computed.  Moreover we obtain generalized results including previously established ones.  In particular,  Laplace transform of Dixon elliptic functions are also presented for comparison purposes.  Furthermore, Maple graphs for Dixon elliptic functions and their transforms are plotted are presented.