Quasi associated continued fractions and Hankel determinants of Dixon elliptic functions via Sumudu transform

In this work, Sumudu transform of Dixon elliptic functions for higher arbitrary powers smN(x, α);N ≥ 1, smN(x, α)cm(x, α); N ≥ 0 and sm^N(x, α)cm²(x, α);N ≥ 0 by considering modulus α ≠ 0 is obtained as three term recurrences and hence expanded as product of quasi associated continued fractions where the coefficients are functions of α. Secondly the coefficients of quasi associated continued fractions are used for Hankel determinants calculations by connecting the formal power series (Maclaurin series) and associated continued fractions.