Elliptic functions


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Related to Elliptic functions: Jacobi's elliptic functions
a large and important class of functions, so called because one of the forms expresses the relation of the arc of an ellipse to the straight lines connected therewith.

See also: Function

References in periodicals archive ?
Drawing upon deep intuition, Ramanujan created new concepts in the theory of numbers, elliptic functions and infinite series.
Miller, "Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs," Journal of Symbolic Computation, vol.
To simplify the dynamic modelling the mass is concentrated at the center of the beam and exact solution is given in terms of elliptic functions.
They find that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions, and that these formulae are consistent with predictions of Whitham's formal modulation theory in both the hyperbolic and elliptic cases.
By virtue of the residue theorem of elliptic functions, we have
FLAJOLET, Pseudo-factorials, elliptic functions, and continued fractions, arXiv:0901.
The 11 papers in this collection review the role of nontrivial symmetries in equilibrium thermodynamics, the Lie derivative of spinor fields, Landen transformation formulas for Jacobi elliptic functions, and the quantum electrodynamics of the Poincare group.
Here, dn(z; [beta]) and cn(z; [beta]) are the Jacobian elliptic functions for z = [alpha](x - [x.
2 and Maple 11 both appealed to the use of elliptic functions (F and Pi) over the complex domain, while the TI-89 gave no result.
The close connection between q-calculus on the one hand, and elliptic functions and theta functions on the other hand will be shown.
In case that the spectrum is not well represented by the elliptic functions region, a more general development by Starke [33] describes how generalized Leja points yield asymptotically optimal iteration parameters.

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