Transcendence Certificates for D-finite Functions
Open Access
- 24 July 2023
- conference paper
- Published by Association for Computing Machinery (ACM)
- p. 372-380
Abstract
Although in theory we can decide whether a given D-finite function is transcendental, transcendence proofs remain a challenge in practice. Typically, transcendence is certified by checking certain incomplete sufficient conditions. In this paper we propose an additional such condition which catches some cases on which other tests fail.Keywords
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Funding Information
- Austrian Science Fund (I6130-N,P31571-N32,P34872-N)
This publication has 18 references indexed in Scilit:
- Reduction-based creative telescoping for fuchsian D-finite functionsJournal of Symbolic Computation, 2018
- Integral D-Finite Functions2015
- Analytic Combinatorics2009
- Note on algebraic solutions of differential equations with known finite Galois groupApplicable Algebra in Engineering, Communication and Computing, 2005
- A Uniform Approach for the Fast Computation of Matrix-Type Padé ApproximantsSIAM Journal on Matrix Analysis and Applications, 1994
- Galois Groups of Second and Third Order Linear Differential EquationsJournal of Symbolic Computation, 1993
- Monodromy for the hypergeometric function n F n ?1Inventiones Mathematicae, 1989
- An algorithm for solving second order linear homogeneous differential equationsJournal of Symbolic Computation, 1986
- The reciprocals of solutions of linear ordinary differential equationsAdvances in Mathematics, 1985
- On Second Order Linear Differential Equations with Algebraic SolutionsAmerican Journal of Mathematics, 1979