Sur la somme de certaines séries de factorielles

Moulay A. Barkatou; Anne Duval

Annales de la Faculté des sciences de Toulouse : Mathématiques (1997)

  • Volume: 6, Issue: 1, page 7-58
  • ISSN: 0240-2963

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Barkatou, Moulay A., and Duval, Anne. "Sur la somme de certaines séries de factorielles." Annales de la Faculté des sciences de Toulouse : Mathématiques 6.1 (1997): 7-58. <http://eudml.org/doc/73414>.

@article{Barkatou1997,
author = {Barkatou, Moulay A., Duval, Anne},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Gevrey series; multi-summable series; factorial series; Mellin transformation; formal solutions; difference equations},
language = {fre},
number = {1},
pages = {7-58},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Sur la somme de certaines séries de factorielles},
url = {http://eudml.org/doc/73414},
volume = {6},
year = {1997},
}

TY - JOUR
AU - Barkatou, Moulay A.
AU - Duval, Anne
TI - Sur la somme de certaines séries de factorielles
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1997
PB - UNIVERSITE PAUL SABATIER
VL - 6
IS - 1
SP - 7
EP - 58
LA - fre
KW - Gevrey series; multi-summable series; factorial series; Mellin transformation; formal solutions; difference equations
UR - http://eudml.org/doc/73414
ER -

References

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  2. [2] Batchelder ( P.-M.) . — An introduction to linear difference equations, Harvard university Press, Cambridge, 1927. JFM53.0430.09
  3. [3] Balser ( W.), Braaksma ( B. L. J), Ramis ( J.-P.) et Sibuya ( Y.) .— Multisummability of formal power series solutions of linear ordinary differential equations, Asymtotic Analysis, 5 (1991), pp. 27-45, 19991. Zbl0754.34057MR1132079
  4. [4] Barkatou ( M.A.) et Duval ( A.) .— Sur les séries formelles solutions d'équations aux différences polynomiales, Ann. Inst. Fourier44, n° 2 (1994). Zbl0803.39005MR1296741
  5. [5] Borel ( E.) . — Leçons sur les séries divergentes, Gauthier-Villars, Paris, seconde édition, 1928. JFM54.0223.01
  6. [6] Ecalle ( J.) .— Les fonctions résurgentes, Tome 3, Publications Mathématiques d'Orsay 85-05 (1985). Zbl0602.30029MR852210
  7. [7] Fitzpatrick ( W.J.) et Grimm ( L.J.). — Convergent factorial series solutions of linear difference equations, J. Diff Equations29 (1978), pp. 345-361. Zbl0403.39001MR507483
  8. [8] Gérard ( R.) et Lutz ( D.) .— Convergent factorial series solutions of singular operators equations, Analysis10 (1990), pp. 99-145. Zbl0712.39016MR1074828
  9. [9] Immink ( G.K.) .— On the summability of the formal solutions of a class of homogeneous linear difference équations, Preprint of the university of Groningen1993 (cf. 1.5). 
  10. [10] Malgrange ( B.) .— Sommation des séries divergentes, Expositiones Mathematicae, Expo. Math.13 (1995), pp. 163-222. Zbl0836.40004MR1346201
  11. [11] Martinet ( J.) et Ramis ( J.-P.) .— Elementary acceleration and multisummabilityAnn. Inst. Henri Poincaré, Physique Théorique, 54 (1991), pp. 331-401. Zbl0748.12005MR1128863
  12. [12] Nörlund ( N.-E.) .— Leçons sur les séries d'interpolation, Gauthiers Villars et Cie, Paris1926. JFM52.0301.04
  13. [13] Nörlund ( N.-E.) .— Leçons sur les Equations linéaires aux différences finies, Gauthiers Villars et CieParis1929. JFM55.0869.01
  14. [14] Nörlund ( N.-E.) .— Vorlesungen über Differenzenrechnung, Springer VerlagBerlin1924. JFM50.0315.02
  15. [15] Olver ( F.W.J.) .— Asymptotics and Special Functions, Academic Press1974. Zbl0303.41035MR435697
  16. [16] Ramis ( J.-P.) .— Divergent series and holomorphic dynamical systems, In Bifurcations et orbites périodiques des champs de vecteurs; Séminaires scientifiques OTAN (1993) NATO-ASI. MR1272100
  17. [17] Wasow ( W.) .— Asymptotic Expansions For Ordinary Differential Equations, Interscience PublishersNew-York1965. Zbl0133.35301MR203188

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