# Accelero-summation of the formal solutions of nonlinear difference equations

Geertrui Klara Immink^{[1]}

- [1] University of Groningen Faculty of Economics P.O. Box 800 9700 AV Groningen (The Netherlands)

Annales de l’institut Fourier (2011)

- Volume: 61, Issue: 1, page 1-51
- ISSN: 0373-0956

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topImmink, Geertrui Klara. "Accelero-summation of the formal solutions of nonlinear difference equations." Annales de l’institut Fourier 61.1 (2011): 1-51. <http://eudml.org/doc/219670>.

@article{Immink2011,

abstract = {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 “level $1^+$”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain.},

affiliation = {University of Groningen Faculty of Economics P.O. Box 800 9700 AV Groningen (The Netherlands)},

author = {Immink, Geertrui Klara},

journal = {Annales de l’institut Fourier},

keywords = {Nonlinear difference equation; formal solution; accelero-summation; quasi-function; nonlinear difference equation},

language = {eng},

number = {1},

pages = {1-51},

publisher = {Association des Annales de l’institut Fourier},

title = {Accelero-summation of the formal solutions of nonlinear difference equations},

url = {http://eudml.org/doc/219670},

volume = {61},

year = {2011},

}

TY - JOUR

AU - Immink, Geertrui Klara

TI - Accelero-summation of the formal solutions of nonlinear difference equations

JO - Annales de l’institut Fourier

PY - 2011

PB - Association des Annales de l’institut Fourier

VL - 61

IS - 1

SP - 1

EP - 51

AB - 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 “level $1^+$”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum is an analytic solution of the equation, represented asymptotically by the formal solution in a certain unbounded domain.

LA - eng

KW - Nonlinear difference equation; formal solution; accelero-summation; quasi-function; nonlinear difference equation

UR - http://eudml.org/doc/219670

ER -

## References

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