منابع مشابه
Heun equations coming from geometry 1
We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers done by Herfurtner. We also show that pullbacks of hypergeometric functions by rational Belyi functions with restricted ramification data give rise to Heun equations.
متن کاملNew transformation law for Heun and Hypergeometric Equations
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.
متن کاملInce’s limits for confluent and double-confluent Heun equations
We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and conv...
متن کاملSolving systems of transcendental equations involving the Heun functions
The Heun functions have wide application in modern physics and are expected to succeed the hypergeometrical functions in the physical problems of the 21st century. The numerical work with those functions, however, is complicated and requires filling the gaps in the theory of the Heun functions and also, creating new algorithms able to work with them efficiently. We propose a new algorithm for s...
متن کاملReal Solutions to Equations from Geometry
Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a very difficult problem with many applications. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure. Particularly fruitful—both for information on real solutions and for applicability—are systems who...
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ژورنال
عنوان ژورنال: Bulletin of the Brazilian Mathematical Society, New Series
سال: 2012
ISSN: 1678-7544,1678-7714
DOI: 10.1007/s00574-012-0020-4