Hankel Determinants of Non-Zero Modulus Dixon Elliptic Functions via Quasi C Fractions
Rathinavel Silambarasan,Adem Kilicman +1 more
- Vol. 3, Iss: 2, pp 22
TLDR
In this paper, 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.Abstract:
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.read more
References
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Analytic Theory of Continued Fractions
TL;DR: In this article, a convergence theory of positive definite continued fractions is presented. But the convergence theory is not a generalization of the Stieltjes convergence theorem, and the convergence of continued fractions whose partial denominators are equal to unity is not discussed.
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TL;DR: In this paper, Jacobi's Zeta and Epsilon functions are presented as functions of the squared modulus of the Equation (1) of the Squared Modulus.
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Continued Fractions: Analytic Theory and Applications
William B. Jones,W. J. Thron +1 more
TL;DR: In this paper, the authors present a method for representing analytic functions by continued fractions and apply it to the birth-death process (BDP) in the context of continuous fractions.
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Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions
TL;DR: Andrews as discussed by the authors derived infinite families of non-trivial exact exact formulas for sums of squares by combining a variety of methods and observations from the theory of Jacobi elliptic functions, continued fractions, Hankel or Turanian determinants, Lie algebras, Schur functions, and multiple basic hypergeometric series related to the classical groups.
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