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

2017 ◽  
Vol 10 (07) ◽  
pp. 4000-4014 ◽  
Author(s):  
Adem Kilicman ◽  
Rathinavel Silambarasan ◽  
Omer Altun
Keyword(s):  
Continued Fractions ◽  
Elliptic Functions ◽  
Hankel Determinants ◽  
Sumudu Transform ◽  
Associated Continued Fractions

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

2019 ◽  
Vol 3 (2) ◽  
pp. 22
Author(s):  
Rathinavel Silambarasan ◽  
Adem Kılıçman
Keyword(s):  
Power Series ◽  
Laplace Transform ◽  
Formal Power Series ◽  
Elliptic Function ◽  
Elliptic Functions ◽  
Maclaurin Series ◽  
Hankel Determinants ◽  
The Laplace Transform ◽  
Sumudu Transform ◽  
Formal Power

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.

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

2018 ◽  
Author(s):  
Adem Kilicman ◽  
Rathinavel Silambarasan
Keyword(s):  
Power Series ◽  
Laplace Transform ◽  
Formal Power Series ◽  
Elliptic Function ◽  
Elliptic Functions ◽  
Maclaurin Series ◽  
Hankel Determinants ◽  
The Laplace Transform ◽  
Sumudu Transform ◽  
Formal Power

Sumudu transform of the Dixon elliptic function with non zero modulus a ≠ 0 for arbitrary powers smN(x,a) ; N ≥ 1 ; smN(x,a)cm(x,a) ; N ≥ 0 and smN(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).

scholarly journals Pseudo-factorials, elliptic functions, and continued fractions

2009 ◽  
Vol 21 (1) ◽  
pp. 71-97 ◽  
Author(s):  
Roland Bacher ◽  
Philippe Flajolet
Keyword(s):  
Continued Fractions ◽  
Elliptic Functions

scholarly journals ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

2017 ◽  
Vol 13 (2) ◽  
pp. 7147-7154
Author(s):  
Anthony G Shannon ◽  
Charles K Cook b ◽  
Rebecca A. Hillman c
Keyword(s):  
Continued Fractions ◽  
Arbitrary Order ◽  
Fibonacci Numbers ◽  
Recursive Sequences ◽  
Essential Idea ◽  
Associated Continued Fractions ◽  
Generalized Continued Fractions

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements.

Continued Logarithms and Associated Continued Fractions

2016 ◽  
Vol 26 (4) ◽  
pp. 412-429
Author(s):  
Jonathan M. Borwein ◽  
Neil J. Calkin ◽  
Scott B. Lindstrom ◽  
Andrew Mattingly
Keyword(s):  
Continued Fractions ◽  
Associated Continued Fractions
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