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Название: Solutions of linear ordinary differential equasions in terms of special functions
Авторы: Bronstein M., Lafaille S.
We describe a new algorithm for computing special function solutions of the form y(x) = in(x)F(£(x)) of second order linear ordinary differential equations, where m(x) is an arbitrary Liouvillian function, £(x) is an arbitrary rational function, and F satisfies a given second order linear ordinary differential equation. Our algorithm, which is based on finding an appropriate point transformation between the equation defining F and the one to solve, is able to find all rational transformations for a large class of functions F, in particular (but not only) the 0F1 and i-Fi special functions of mathematical physics, such as Airy, Bessel, Kumruer and
Whit taker functions. It is also able to identify the values of the parameters entering those special functions, and can be generalized to equations of higher order.