Generalized trigonometric identities and invariant imbedding

Generalized Invariant Imbedding Relation.

List of trigonometric identities

Cosines and sines around the unit circle In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities involving both angles and side lengths of a tri...

Fibonacci numbers and trigonometric identities

Webb & Parberry proved in 1969 a startling trigonometric identity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.

Dissipation Functions and Invariant Imbedding, I.

A Generalized Parameter Imbedding Method

The parameter imbedding method for the Fredholm equation converts it into an initial value problem in its parameter λ. We establish the method for general operator equations of the form [I + ˆ f (λ)]ψ = φ. It is particularly useful for studying spontaneous symmetry breaking problems, such as contained in the nonlinear Schwinger-Dyson equation.