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
The elliptic functions
can be used to create the highest selective filters .
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  describes how generalized Leja points yield asymptotically optimal iteration parameters.