Appell Hypergeometric Expansions of the Solutions of the General Heun Equation
نویسندگان
چکیده
منابع مشابه
On Reducing the Heun Equation to the Hypergeometric Equation
The reductions of the Heun equation to the hypergeometric equation by rational transformations of its independent variable are enumerated and classified. Heun-tohypergeometric reductions are similar to classical hypergeometric identities, but the conditions for the existence of a reduction involve features of the Heun equation that the hypergeometric equation does not possess; namely, its cross...
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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...
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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.
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ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2018
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-018-9424-8