Sumudu Transform of Dixon Elliptic Functions With Non-Zero Modulus as Quasi C Fractions and Its Hankel Determinants

Adem Kilicman; Rathinavel Silambarasan

doi:10.20944/preprints201806.0095.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 6 June 2018 / Approved: 6 June 2018 / Online: 6 June 2018 (13:05:28 CEST)

Sumudu transform of the Dixon elliptic function with non zero modulus a ≠ 0 for arbitrary powers sm^N(x,a) ; N ≥ 1 ; sm^N(x,a)cm(x,a) ; N ≥ 0 and sm^N(x,a)cm²(x,a) ; N ≥ 0 is given by product of Quasi C fractions. Next by assuming denominators of Quasi C fraction to 1 and hence applying Heliermann correspondance relating formal power series (Maclaurin series of Dixon elliptic functions) and regular C fraction, Hankel determinants are calculated and showed by taking a = 0 gives the Hankel determinants of regular C fraction. The derived results were back tracked to the Laplace transform of sm(x,a) ; cm(x,a) and sm(x,a)cm(x,a).

dixon elliptic functions; non-zero modulus; sumudu transform; hankel determinants; continued fractions; Quasi C fractions

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Sumudu Transform of Dixon Elliptic Functions With Non-Zero Modulus as Quasi C Fractions and Its Hankel Determinants

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