Approximants de Padé et U -dérivation

Daniel Duverney

Bulletin de la Société Mathématique de France (1994)

  • Volume: 122, Issue: 4, page 553-570
  • ISSN: 0037-9484

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Duverney, Daniel. "Approximants de Padé et $U$-dérivation." Bulletin de la Société Mathématique de France 122.4 (1994): 553-570. <http://eudml.org/doc/87704>.

@article{Duverney1994,
author = {Duverney, Daniel},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Padé approximants; -derivation; orthogonal polynomials; Padé table; formal series; approximants},
language = {fre},
number = {4},
pages = {553-570},
publisher = {Société mathématique de France},
title = {Approximants de Padé et $U$-dérivation},
url = {http://eudml.org/doc/87704},
volume = {122},
year = {1994},
}

TY - JOUR
AU - Duverney, Daniel
TI - Approximants de Padé et $U$-dérivation
JO - Bulletin de la Société Mathématique de France
PY - 1994
PB - Société mathématique de France
VL - 122
IS - 4
SP - 553
EP - 570
LA - fre
KW - Padé approximants; -derivation; orthogonal polynomials; Padé table; formal series; approximants
UR - http://eudml.org/doc/87704
ER -

References

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  1. [1] ALLADI (K.) and ROBINSON (M.L.). — Legendre Polynomials and Irrationality, J. Reine Angew. Math., t. 318, 1980, p. 137-155. Zbl0425.10039MR81i:10036
  2. [2] BORWEIN (P.). — Padé Approximants for the q-Elementary Functions, Constr. Approx., t. 4, 1988, p. 391-402. Zbl0685.41015MR89f:41022
  3. [3] BORWEIN (P.). — On the Irrationality of ∑(1/(qn + r)), J. Number Theory, t. 37, 1991, p. 253-259. Zbl0718.11029MR92b:11046
  4. [4] BREZINSKI (C.). — Padé-type Approximation and General Orthogonal Polynomials. — Birkhäuser, 1980. Zbl0418.41012MR82a:41017
  5. [5] BREZINSKI (C.) and VAN ISEGHEM (J.). — Padé Approximations, Handbook of Numerical Analysis. — P.G. Ciarlet and J.L. Lions ed., North Holland, 1992. 
  6. [6] DUVERNEY (D.). — U-Dérivation. — Annales Fac. Sci. Toulouse, série 6, vol II, fasc. 3, 1993, p. 323-335. Zbl0803.12003MR94m:12008
  7. [7] EXTON (M.). — q-Hypergeometric Functions and Applications, Chichester, 1983. Zbl0514.33001
  8. [8] GASPER (G.) and RAHMAN (M.). — Basic Hypergeometric Series. — Cambridge University Press, 1990. Zbl0695.33001MR91d:33034
  9. [9] LUKE (Y.L.). — The Special Functions and their Approximations. — Academic Press, 1969. Zbl0193.01701
  10. [10] PADÉ (H.). — Sur les développements en fractions continues de la fonction F(h, 1, h′, u) et la généralisation de la théorie des fonctions sphériques, C.R. Acad. Sci. Paris, t. 141, 1905, p. 819-821. Zbl36.0297.03JFM36.0297.03
  11. [11] THOMAE (J.). — Beiträge zur Theorie der durch die Heinesche Reine..., J. Reine Angew. Math., t. 70, 1869, p. 258-281. JFM02.0122.04
  12. [12] WALLISSER (R.). — Rationale Approximation des q-Analogons der Exponentialfunktion und Irrationalitätsaussagen für diese Funktion, Archiv Math., t. 44, 1985, p. 59-64. Zbl0558.33004MR86i:11036

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