Hankel Determinants of Non-Zero Modulus Dixon Elliptic Functions via Quasi C Fractions

Abstract

The Sumudu transform of the Dixon elliptic function with non-zero modulus alpha not equal 0 for arbitrary powers N is given by the product of quasi C fractions. Next, by assuming the denominators of quasi C fractions as one and applying the Heliermanncorrespondence relating formal power series (Maclaurin series of the Dixon elliptic function) and the regular C fraction, the Hankel determinants are calculated for the non-zero Dixon elliptic functions and shown by taking alpha = 0 to give the Hankel determinants of the Dixon elliptic function with zero modulus. The derived results were back-tracked to the Laplace transform of Dixon elliptic functions.