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Publications Influence

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

10 3

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

11 2- PDF

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

4 1

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

15 1- PDF

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.

40

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

5- PDF

Differential equations and the Stokes Phenomenon

- B. Braaksma, G. K. Immink, J. Top, M. Put
- Mathematics
- 2002

22

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

16

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

15

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

7- PDF