Power series expansions for Mathieu functions with small arguments

Power series expansions for Mathieu functions with small arguments

Power series expansions for the even and odd angular Mathieu functions Sem(h, cos θ) and Som(h, cos θ), with small argument h, are derived for general integer values of m. The expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind.

New method to obtain small parameter power series expansions of Mathieu radial and angular functions

Small parameter power series expansions for both radial and angular Mathieu functions are derived. The expansions are valid for all integer orders and apply the Stratton-Morse-Chu normalization. Three new contributions are provided: (1) explicit power series expansions for the radial functions, which are not available in the literature; (2) improved convergence rate of the power series expansio...

The Asymptotic Expansions for the Qdd Periodic Mathieu Functions

Basis Construction from Power Series Expansions of Value Functions

This paper explores links between basis construction methods in Markov decision processes and power series expansions of value functions. This perspective provides a useful framework to analyze properties of existing bases, as well as provides insight into constructing more effective bases. Krylov and Bellman error bases are based on the Neumann series expansion. These bases incur very large in...

Quasi-orthogonal expansions for functions in BMO

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M