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

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Department of Information Technology, School of Information Technology and Engineering, Vellore Institute of Technology, Vellore 632014, India
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Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia
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Department of Electrical and Electronic Engineering, Istanbul Gelisim University, Istanbul 34310, Turkey
*
Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 22; https://doi.org/10.3390/fractalfract3020022
Received: 5 March 2019 / Revised: 12 April 2019 / Accepted: 12 April 2019 / Published: 17 April 2019
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. View Full-Text
Keywords: Dixon elliptic functions; Sumudu transform; Hankel determinants; continued fractions; quasi C fractions Dixon elliptic functions; Sumudu transform; Hankel determinants; continued fractions; quasi C fractions
MDPI and ACS Style

Silambarasan, R.; Kılıçman, A. Hankel Determinants of Non-Zero Modulus Dixon Elliptic Functions via Quasi C Fractions. Fractal Fract 2019, 3, 22.

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