ABSTRACT

A series expansion in terms of parabolic cylinder functions to the Biconuent Heun equation (BHE) is given. The orthogonality of eigen-solutions with finite sum of parabolic functions is discussed. Based on an observation that both the Bessel equation and the BHE have a regular singular point at the origin and an irregular singular point at infinity on the Riemann sphere C, and that the former equation has orthogonal polynomial solutions with respect to a complex weight, we investigate the existence of eigen-solutions of polynomials related to the BHE. Orthogonal property of these polynomials is discussed with complex weight. This is a joint work with Yik-Man Chiang and Chun-Kong Law.