Study of the properties of Zernike's orthogonal polynomials

摘要

Wide application of Zernike's orthogonal polynomials at lens design and optical engineering generates a need of more detailed study of their properties, assemblage new results and results received previously. In this connection we bring results of our researches on study of properties of Zernike's polynomials, revealing their interrelation with other special functions, obtaining recurrence relations, formulas of differentiation of Zernike's radial polynomials, decomposition of the ratio of two radial polynomials in continuous fractions and so on.