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

Volume 10, Issue 7, pp 4000--4014 http://dx.doi.org/10.22436/jnsa.010.07.49

Publication Date: July 27, 2017 Submission Date: February 11, 2017

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Authors

Adem Kilicman - Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia. Rathinavel Silambarasan - M. Tech IT-Networking, Department of Information Technology, School of Information Technology and Engineering, VIT University, Vellore, Tamilnadu, India. Omer Altun - Department of Mathematics and Institute for Mathematical research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

Abstract

In this work, Sumudu transform of Dixon elliptic functions for higher arbitrary powers \(sm^N(x, \alpha);N \geq 1, sm^N(x, \alpha)cm(x, \alpha); N \geq 0\) and \(sm^N(x, \alpha)cm^2(x, \alpha);N \geq 0\) by considering modulus \(\alpha \neq 0\) is obtained as three term recurrences and hence expanded as product of quasi associated continued fractions where the coefficients are functions of \(\alpha\). 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.

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Keywords

• Dixon elliptic functions
• quasi associated continued fractions
• Hankel determinants
• Sumudu transform
• three term recurrence.

MSC

•  11A55
•  11C20
•  33E05
•  44A10

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