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Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]
Commun Math PhysDorigoni D +7 more
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Phase-lag mixed integral equation of a generalized symmetric potential kernel and its physical meanings in (3+1) dimensions. [PDF]
HeliyonJan AR.
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Chaotic analysis, hopf bifurcation and collision of optical periodic solitons in (2+1)-dimensional degenerated Biswas-Milovic equation with Kerr law of nonlinearity. [PDF]
Sci RepAl-Sawalha MM, Noor S, Shah R, Yasmin H.
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Expression of Elliptic Functions in Terms of Jacobi Functions
Russian Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2020
Jacobi elliptic functions are a realization of one of the simplest cases of elliptic functions, as described in Chapter 14: functions with two simple poles in a period parallelogram that are odd around each pole. These functions come up naturally in certain problems of mechanics, such as the motion of an ideal pendulum.
Richard Beals, Roderick S. C. Wong
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Jacobi elliptic functions are a realization of one of the simplest cases of elliptic functions, as described in Chapter 14: functions with two simple poles in a period parallelogram that are odd around each pole. These functions come up naturally in certain problems of mechanics, such as the motion of an ideal pendulum.
Richard Beals, Roderick S. C. Wong
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2021
Topic of this chapter are the Jacobi elliptic functions sn, cn, dn, their first derivatives, the additional nine Jacobi elliptic functions, and the amplitude function am. The evaluation of the Jacobi elliptic functions is based on the Jacobi đťś— functions and in case of convergency issues additionally on the Gauss hypergeometric function.
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Topic of this chapter are the Jacobi elliptic functions sn, cn, dn, their first derivatives, the additional nine Jacobi elliptic functions, and the amplitude function am. The evaluation of the Jacobi elliptic functions is based on the Jacobi đťś— functions and in case of convergency issues additionally on the Gauss hypergeometric function.
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A structurally stable realization for Jacobi elliptic functions
2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), 2003By adding convergence terms, the dynamical equations for the generation of elliptic functions versus time are presented. This results in a structurally stable oscillator with limit cycles, which are Jacobi elliptic functions. From these equations a CMOS realization is developed with the nonlinearities obtained by using analog four-quadrant multipliers ...
Honghao Ji, R. W. Newcomb
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On Jacobi’s transformation theory of elliptic functions
Archive for History of Exact Sciences, 2013The modern theory of elliptic functions was created during a historical race between Abel and Jacobi. Whereas the publications of Abel have been studied extensively (see, e.g. [\textit{C. Houzel}, in: The legacy of Niels Henrik Abel. Papers from the Abel bicentennial conference, University of Oslo, Oslo, Norway, 2002. Berlin: Springer.
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1989
The elliptic functions sn u, cn u, and dn u are defined as ratios of theta functions as below: $$sn\;u = \frac{{{\theta _3}(0)}}{{{\theta _2}(0)}}\cdot \frac{{{\theta _1}(z)}}{{{\theta _4}(z)}},$$ (2.1.1) $$cn\,u = \frac{{{\theta _4}(0)}}{{{\theta _2}(0)}}\cdot \frac{{{\theta _2}(z)}}{{{\theta _4}(z)}},$$ (2.1.2) $$dn\;u = \frac{
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The elliptic functions sn u, cn u, and dn u are defined as ratios of theta functions as below: $$sn\;u = \frac{{{\theta _3}(0)}}{{{\theta _2}(0)}}\cdot \frac{{{\theta _1}(z)}}{{{\theta _4}(z)}},$$ (2.1.1) $$cn\,u = \frac{{{\theta _4}(0)}}{{{\theta _2}(0)}}\cdot \frac{{{\theta _2}(z)}}{{{\theta _4}(z)}},$$ (2.1.2) $$dn\;u = \frac{
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