The reciprocals of solutions of linear ordinary differential equations

DOI10.1016/0001-8708(85)90113-6zbMath0581.12013OpenAlexW1995331565MaRDI QIDQ1068138

Yasutaka Sibuya, William A. jun. Harris

Publication date: 1985

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(85)90113-6

zbMATH Keywords

linear ordinary differential equationsformal power seriesexponentialpartial differential fieldordinary fieldPicard-Vessiot elements

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Linear differential equations in abstract spaces (34G10) Differential algebra (12H05)

Related Items (11)

On the algebraic dependence of holonomic functions ⋮ D-finite numbers ⋮ Logarithmic derivatives of solutions to linear differential equations ⋮ On primary pseudo-polynomials (around Ruzsa’s conjecture) ⋮ Transcendence Certificates for D-finite Functions ⋮ Three friendly walkers ⋮ Formulae and Asymptotics for Coefficients of Algebraic Functions ⋮ Free subgroups of free products and combinatorial hypermaps ⋮ Dynamics on abelian varieties in positive characteristic ⋮ Algebraic Relations Among Solutions of Linear Differential Equations ⋮ Inverse for the shuffle for algebraic series

Cites Work

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• Power series solutions of algebraic differential equations
• Differentiably finite power series
• Associative differential operations
• The Coefficients of the Reciprocal of a Bessel Function

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