منابع مشابه
On 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 کاملPolynomial 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 کاملOn Spectral Polynomials of the Heun
The well-known Heun equation has the form { Q(z) d2 dz2 + P (z) d dz + V (z) } S(z) = 0, where Q(z) is a cubic complex polynomial, P (z) and V (z) are polynomials of degree at most 2 and 1 respectively. One of the classical problems about the Heun equation suggested by E. Heine and T. Stieltjes in the late 19-th century is for a given positive integer n to find all possible polynomials V (z) su...
متن کاملMoment Tensor Potentials: A Class of Systematically Improvable Interatomic Potentials
Density functional theory offers a very accurate way of computing materials properties from first principles. However, it is too expensive for modeling large-scale molecular systems whose properties are, in contrast, computed using interatomic potentials. The present paper considers, from a mathematical point of view, the problem of constructing interatomic potentials that approximate a given q...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2013
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/46/24/245204