Equivalence of differential operators
SIAM Journal on Mathematical Analysis
Hypergeometric functions and their applications
Hypergeometric functions and their applications
Finding all hypergeometric solutions of linear differential equations
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
An extensible differential equation solver
ACM SIGSAM Bulletin
Solutions of linear ordinary differential equations in terms of special functions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Solving second order linear differential equations with Klein's theorem
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Solving differential equations in terms of bessel functions
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
| Hi-index | 0.00 |
There exist sound literature and algorithms for computing Liouvillian solutions for the important problem of linear ODEs with rational coefficients. Taking as sample the 363 second order equations of that type found in Kamke's book, for instance, 51% of them admit Liouvillian solutions and so are solvable using Kovacic's algorithm. On the other hand, special function solutions not admitting Liouvillian form appear frequently in mathematical physics, but there are not so general algorithms for computing them. In this paper we present an algorithm for computing special function solutions which can be expressed using the ;2;F;1;, ;1;F;1; or ;0;F;1; hypergeometric functions. The algorithm is easy to implement in the framework of a computer algebra system and systematically solves 91% of the 363 Kamke's linear ODE examples mentioned.