Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Prof. Alexi Zhedanov, 中国人民大学
The Heun linear pencil as a universal tool for exactly and quasi-exactly solvable problems
Time & Venue:
2018.4.20 15:00-16:00 N210
The Heun linear pencil is the most general bilinear operator which can be constructed from a pair of bispectral operators. In the case if one of these operators is the hypergeometric operator the Heun pencil coincides with the ordinary Heun operator. For other choices of the pair of bisopectral operators we obtain generalizations of the Heun operator, including q-Heun operators. The Heun pencil is related with the method of tridiagonalization. In special cases the Heun pencil allows to obtain the Racah-Wilson operator (and corresponding orthogonal polynomials) from the Gauss hypergeometric operator. Applications of the Heun pencil to problems in mathematical physics are considered.
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