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TitleGuessing singular dependencies
Author(s) Joris van der Hoeven
TypeArticle in Journal
AbstractAbstract Given d complex numbers z_1 , … , z_d , it is classical that linear dependencies λ_1 z_1 + ⋯ + λ_d z_d = 0 with λ_1 , … , λ_d ∈ Z can be guessed using the LLL-algorithm. Similarly, given d formal power series f_1 , … , f_d ∈ C [ [ z ] ] , algorithms for computing Padé–Hermite forms provide a way to guess relations P_1 f_1 + ⋯ + P_d f_d = 0 with P_1 , … , P_d ∈ C [ z ] . Assuming that f_1 , … , f_d have a radius of convergence r > 0 and given a real number R > r , we will describe a new algorithm for guessing linear dependencies of the form g_1 f_1 + ⋯ + g_d f_d = h , where g_1 , … , g_d , h ∈ C [ [ z ] ] have a radius of convergence ≥R. We will also present two alternative algorithms for the special cases of algebraic and Fuchsian dependencies.
KeywordsGuessing, Asymptotic dependency, Orthogonalization, Analytic continuation, Fuchsian singularity, Padé–Hermite forms, Algorithm
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717113000977
LanguageEnglish
JournalJournal of Symbolic Computation
Volume59
Number0
Pages54 - 80
Year2013
Edition0
Translation No
Refereed No
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