Hypergeometric Expansions of Heun Polynomials
نویسندگان
چکیده
منابع مشابه
On 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...
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In this work we establish new forms of Heun-to-Heun transformations and Heun-to-Hypergeometric transformations. The transformations are realised by changing the independent variable in a non-linear way. Using these we also point out some simple examples of transformations between equations that are not Fuchsian and that generalise the Heun-toHypergeometric transformations.
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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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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 1991
ISSN: 0036-1410,1095-7154
DOI: 10.1137/0522093