منابع مشابه
Polynomial Solutions of the Heun Equation
We review properties of certain types of polynomial solutions of the Heun equation. Two aspects are particularly concerned, the interlacing property of spectral and Stieltjes polynomials in the case of real roots of these polynomials and asymptotic root distribution when complex roots are present.
متن کاملThe 192 solutions of the Heun equation
A machine-generated list of 192 local solutions of the Heun equation is given. They are analogous to Kummer’s 24 solutions of the Gauss hypergeometric equation, since the two equations are canonical Fuchsian differential equations on the Riemann sphere with four and three singular points, respectively. Tabulation is facilitated by the identification of the automorphism group of the equation wit...
متن کاملIntegral relations for solutions of the confluent Heun equation
Abstract: Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions. Thirdly, by using one of the integral rel...
متن کاملOn the Heun equation.
A new approach to the theory of finite-gap integration for the Heun equation is constructed. As an application, global monodromies of the Heun equation are calculated and expressed as hyperelliptic integrals. The relationship between the Heun equation and the spectral problem for the BC1 Inozemtsev model is also discussed.
متن کاملTransforming the Heun Equation to the Hypergeometric Equation: I. Polynomial Transformations
The reductions of the Heun equation to the hypergeometric equation by rational changes of its independent variable are classified. Heun-to-hypergeometric transformations are analogous to the classical hypergeometric identities (i.e., hypergeometric-to-hypergeometric transformations) of Goursat. However, a transformation is possible only if the singular point location parameter and normalized ac...
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ژورنال
عنوان ژورنال: Acta Polytechnica
سال: 2011
ISSN: 1805-2363,1210-2709
DOI: 10.14311/1416