Computing Hankel Determinants Hm(2) of Dixon Elliptic Functions With Modulus α = 0 Using Regular C Fraction

Abstract

In this research paper Dixon elliptic functions (DEF) having modulus, α = 0, smN(x,0): N ≥ 1 smN(x,0)cm(x,0) and smN(x,0)cm(x,0): N ≥ 0 are expanded by Regular C fractions and generalized using the Sumudu transform. Then Hankel determinants Hm(2) of DEF are calculated without resort to Maclaurin's series. For this purpose Heliermann correspondence is applied to Regular C Fraction (RCF) coefficients. Higher order results are given using formal notation and compact form. Some known and previous results are proven and numerical examples given to check the validity in light of this paper's new findings. © (2025), (Cambridge Scientific Publishers). All rights reserved.