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A particular type of summability of divergent power series, with an application to difference equations
- G. K. Immink
- Mathematics
- 2001
We define a "weak Borel-sum" for a class of formal power series. This is a generalization of the ordinary Borel-sum with applications in the theory of locally analytic difference equations. We… Expand
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Accelero-summation of the formal solutions of nonlinear difference equations
- G. K. Immink
- Mathematics
- 2011
In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of… Expand
ON THE RELATION BETWEEN GLOBAL PROPERTIES OF LINEAR DIFFERENCE AND DIFFERENTIAL-EQUATIONS WITH POLYNOMIAL COEFFICIENTS .1.
- G. K. Immink
- Mathematics
- 1 October 1994
This paper is the second one in a series of three articles dealing with applications of the Mellin transformation to the theory of linear differential and difference equations with polynomial… Expand
Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$
- G. K. Immink
- Mathematics
- 2008
On etudie une classe d'equations aux differences finies, non-lineaires, possedants une solution formelle en forme de serie 1-Gevrey qui, en general, n'est pas Borel-sommable. En utilisant des… Expand
Asymptotics of Analytic Difference Equations
- G. K. Immink
- Mathematics
- 14 November 1984
Linear difference equations.- Existence proofs for right inverses of difference operators.- Nonlinear difference equations.
On the Relation between Linear Difference and Differential Equations with Polynomial Coefficients
- G. K. Immink
- Mathematics
- 1999
This paper represents the third part of a contribution to the "dictionary" of homogeneous linear differential equations with polynomial coefficients on one hand and corresponding difference equations… Expand
Differential equations and the Stokes Phenomenon
- B. Braaksma, G. K. Immink, J. Top, M. Put
- Mathematics
- 2002
The Stokes phenomenon and Hilbert's 16th problem, Groningen, The Netherlands, 31 May - 3 June 1995
- B. Braaksma, G. K. Immink, M. Put, Hilbert's th problem
- Mathematics
- 1 July 1996
Non-accumulation of limit cycles - revisiting and simplyifyng a former proof followed by construction of a summit-crossing "central trajectory" at semihyperbolic points, J. Ecalle finiteness theorems… Expand
A NOTE ON THE RELATIONSHIP BETWEEN STOKES MULTIPLIERS AND FORMAL SOLUTIONS OF ANALYTIC DIFFERENTIAL-EQUATIONS
- G. K. Immink
- Mathematics
- 1 May 1990
This paper generalizes a result of Balser, Jurkat, and Lutz [J. Math. Anal. Appl., 71 (1979), pp. 48–94] concerning the relation between the Stokes multipliers of a homogeneous linear differential… Expand
The Stokes phenomenon in exact asymptotics
- B. Braaksma, G. K. Immink, Y. Sibuya
- Mathematics
- 1999
As an introduction we present a new, elementary and constructive proof of the multisummability properties of formal solutions of linear ODE's at irregular singular points. This serves to illustrate… Expand