Hankel determinants of non-zero modulus dixon elliptic functions via quasi C fractions

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Silambarasan R., Kılıçman A.

Fractal and Fractional, vol.3, no.2, pp.1-24, 2019 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.3390/fractalfract3020022
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Scopus
  • Page Numbers: pp.1-24
  • Keywords: Continued fractions, Dixon elliptic functions, Hankel determinants, Quasi C fractions, Sumudu transform
  • Istanbul Gelisim University Affiliated: No

Abstract

© 2019 by the authors. Licensee MDPI, Basel, Switzerland.The Sumudu transform of the Dixon elliptic function with non-zero modulus α ̸= 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 α = 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.