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

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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 ITNetworking, 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.
Share and Cite
ISRP Style
Adem Kilicman, Rathinavel Silambarasan, Omer Altun, Quasi associated continued fractions and Hankel determinants of Dixon elliptic functions via Sumudu transform, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 40004014
AMA Style
Kilicman Adem, Silambarasan Rathinavel, Altun Omer, Quasi associated continued fractions and Hankel determinants of Dixon elliptic functions via Sumudu transform. J. Nonlinear Sci. Appl. (2017); 10(7):40004014
Chicago/Turabian Style
Kilicman, Adem, Silambarasan, Rathinavel, Altun, Omer. "Quasi associated continued fractions and Hankel determinants of Dixon elliptic functions via Sumudu transform." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 40004014
Keywords
 Dixon elliptic functions
 quasi associated continued fractions
 Hankel determinants
 Sumudu transform
 three term recurrence.
MSC
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