The Poincaré equation: A new polynomial and its unusual properties

Details The Poincaré equation: A new polynomial and its unusual properties The Poincaré equation: A new polynomial and its unusual properties

Dec 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004jmp....45.4777z&link_type=abstract

Journal of Mathematical Physics, Volume 45, Issue 12, pp. 4777-4790 (2004).

Mathematics

Number Theory

3

Hydrodynamics, Partial Differential Equations, Geometry, Differential Geometry, And Topology, Algebraic Structures And Number Theory, Linear Algebra, Stellar Rotation

Scientific paper

The Poincaré equation, a second-order partial differential equation describing wave motions in a rotating spheroid of arbitrary eccentricity satisfying a certain set of the boundary condition, is studied. A new polynomial as the general solution of the Poincaré equation in spheroidal geometry is found for the first time. The paper focuses on some unusual and intriguing mathematical properties of the new Poincaré polynomial. The possible completeness of the set of eigenfunctions of the Poincaré equation in the form of the new polynomial is also discussed. The new Poincaré polynomial would provide a powerful basis for the mathematical analysis in many important geophysical and astrophysical problems.

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