Stability Problems for D-finite Functions  

Shaoshi Chen (KLMM, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, 100190, China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049, (China)
Ruyong Feng (KLMM, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, 100190, China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049, (China)
*Zewang Guo (KLMM, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, 100190, China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049, (China)
Wei Lu (KLMM, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing, 100190, China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049, (China)

The integration problem for D-finite functions was to compute the order and the defining operator of their integrals. It was studied by Abramov and van Hoeij and the interesting case is that the integral has the same order as the integrand. The main goal of this paper is to investigate Abramov-van Hoeij’s algorithm iteratively.

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