Abstract
This paper addresses necessary and sufficient factorizability conditions for classes of second order linear ordinary differential equations (ODEs) characterized by the degrees of their corresponding polynomial functions coefficients. A pure algebraic method is used to solve a system of linear algebraic equations whose solutions satisfy a compatibility criterion and generate two first order differential operators factorizing the considered second order differential operator. Concrete examples are probed, including special cases of Böcher ODEs like Heun, extensions of Wangerin and Heine’s differential equations.
Funding Statement
This work is partially supported by the Abdus Salam International Centre for Theoretical Physics (ICTP, Trieste, Italy) through the Office of External Activities (OEA)-Prj-15. The ICMPA is in partnership with the Daniel Iagolnitzer Foundation (DIF), France.
Acknowledgements
The authors express their gratitude to referees for their usefull comments which allowed to improve the manuscript.
Citation
M. N. Hounkonnou. P. A. Dkengne Sielenou. "On factorizable classes of second order linear ordinary differential equations with rational functions coefficients." SUT J. Math. 46 (2) 205 - 229, June 2010. https://doi.org/10.55937/sut/1295965316
Information