Computing hypergeometric solutions of second order linear differential equations using quotients of formal solutions and integral bases
Journal of Symbolic Computation, cilt.83, ss.254-271, 2017 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 83
- Basım Tarihi: 2017
- Doi Numarası: 10.1016/j.jsc.2016.11.014
- Dergi Adı: Journal of Symbolic Computation
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.254-271
- Anahtar Kelimeler: Symbolic computation, Linear differential equations, Closed form solutions, Hypergeometric solutions, Integral bases
- Kırklareli Üniversitesi Adresli: Hayır
Özet
We present two algorithms for computing hypergeometric solutions of second order linear differential operators with rational function coefficients. Our first algorithm searches for solutions of the form exp(∫rdx)⋅2F1(a1,a2;b1;f) where r,f∈Q(x)‾, and a1,a2,b1∈Q. It uses modular reduction and Hensel lifting. Our second algorithm tries to find solutions in the form exp(∫rdx)⋅(r0⋅2F1(a1,a2;b1;f)+r1⋅2F1′(a1,a2;b1;f)) where r0,r1∈Q(x)‾, as follows: It tries to transform the input equation to another equation with solutions of type (1), and then uses the first algorithm.