Elsevier

Journal of Symbolic Computation

Volume 85, March–April 2018, Pages 108-127
Journal of Symbolic Computation

Reduction-based creative telescoping for fuchsian D-finite functions

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Abstract

Continuing a series of articles in the past few years on creative telescoping using reductions, we adapt Trager's Hermite reduction for algebraic functions to fuchsian D-finite functions whose singularities have real exponents. We develop a reduction-based creative telescoping algorithm for this class of functions, thereby generalizing our recent reduction-based algorithm for algebraic functions, presented at ISSAC 2016.

Keywords

D-finite function
Integral basis
Trager's reduction
Telescoper

Cited by (0)

S. Chen was supported by the NSFC grants 11501552 and 11688101 and by the President Fund of the Academy of Mathematics and Systems Science, CAS (2014-cjrwlzx-chshsh). M. van Hoeij was supported by the National Science Foundation (NSF) grant 1618657. M. Kauers was supported by the Austrian Science Fund (FWF) grants F50-04 and Y464-N18. C. Koutschan was supported by the Austrian Science Fund (FWF) grant W1214.