Representation of solutions of n-order Riccati equation via generalized trigonometric functions

In this work we suggest a systematic method of construction of solutions of the n-order Riccati equation with constant coefficients in a field from the set of generalized trigonometric functions. The generalized trigonometric functions satisfy the system of evolution equations generated by the companion matrix of n-order polynomial. The set of trigonometric functions depend of (n−1) variables formally expressed by series of exponential functions. In a particular case, the second order Riccati equation with constant coefficients is isomorphic to the evolution equation generated by the companion matrix of the associated quadratic polynomial. It is shown that the n>2 order Riccati equation with coefficients in a field is derived from a linear system of evolution equations generated by companion matrix of the associated n-order polynomial under (n−2) constraints.