@article{AFST_1996_6_S5__121_0, author = {Herbert Stahl}, title = {Diagonal {Pad\'e} approximants to hyperelliptic functions}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {121--193}, publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, S5}, year = {1996}, zbl = {0872.41006}, mrnumber = {1462709}, language = {en}, url = {https://afst.centre-mersenne.org/item/AFST_1996_6_S5__121_0/} }
TY - JOUR AU - Herbert Stahl TI - Diagonal Padé approximants to hyperelliptic functions JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 1996 SP - 121 EP - 193 VL - S5 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/item/AFST_1996_6_S5__121_0/ LA - en ID - AFST_1996_6_S5__121_0 ER -
%0 Journal Article %A Herbert Stahl %T Diagonal Padé approximants to hyperelliptic functions %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 1996 %P 121-193 %V S5 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/item/AFST_1996_6_S5__121_0/ %G en %F AFST_1996_6_S5__121_0
Herbert Stahl. Diagonal Padé approximants to hyperelliptic functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume S5 (1996), pp. 121-193. https://afst.centre-mersenne.org/item/AFST_1996_6_S5__121_0/
[BaGM] Padé Approximants Parts I and Part II, Encycl. Math. Vols 13 and 14. Cambridge University Press, Cambridge (1981).
JR. and -[BGW] An investigation of the applicability of the Padé approximant method, J. Math. Anal. Appl. 2 (1961), pp. 405-418. | MR | Zbl
, and -[Br] History of Continued Fractions and Padé approximants, Series in Comp. Math. 12, Springer-Verlag, Heidelberg (1991). | MR | Zbl
-[Bo] Application des transcendantes abéliennes á la théorie des fractions continues, J. Reine Angew. Math. 48 (1854), pp. 69-104. | Zbl
-[Ch] Analytic Number Theory, Springer-Verlag, Berlin ( 1968).
-[Du] Sur le développement des fonctions elliptiques en fractions continues, Thésis, Univ. Zürich, (1908). | JFM
-[Go] A local condition for single-valuedness of analytic functions, Mat. Sbornik, 89 (131) (1972); English transl. in Math. USSR Sb. 18 ( 1972), pp. 151-167. | MR | Zbl
-[GoRa] Equilibrium distributions and degree of rational approximation of analytic functions , Mat. Sb. 134 ( 1987); English transl. in Math. USSR Sb. 62 ( 1989), pp. 305-48. | MR | Zbl
and -[Ham] Über eine Erweiterung des Stieltjesschen Momentenproblems I, II, III, Math. Ann. 81 (1920). pp. 235-319, Math. Ann. 82 (1921), pp. 120-164, 168-187. | JFM
-[Ha] Traité des fonctions elliptiques et de leurs applications, Tome II. Gauthier-Villars, Paris ( 1888). | JFM
-[Hi] Analytic Function Theory, Ginns and Company, Boston (1962). | MR
-[HuCo] Funktionentheorie, Springer-Verlag, Berlin ( 1929).
and -[Ja] Note sur une nouvelle application de l'analyse des functions elliptiques a l'algèbre, J. Reine Angew. Math. 7 (1830), pp. 41-43. | Zbl
[Kr] The ideas of P. L. Chebychev and A. A. Markov in the theory of limiting values of integrals and their further development, Amer. Math. Soc. Transl. Series 12 (1959), pp. 1-121. | MR | Zbl
-[La] Foundations of Modern Potential Theory , Springer-Verlag Berlin (1972). | MR | Zbl
-[Lu] Divergence of complex rational approximants , Pacific J. Math. 108 (1983), pp. 141-153. | MR | Zbl
-[Nu1] The convergence of Padé approximants of meromorphic functions, J. Math. Anal. Appl. 31 (1970), pp. 129-140. | MR | Zbl
-[Nu2] Asymptotics of diagonal Hermite-Padé polynomials, J. Approx. Theory 42 (1984), pp. 299-386. | MR | Zbl
-[Pe] Die Lehre von den Kettenbrüchen, Teubner, Stuttgard (1913).
-[Po1] POMMERENKE (CH.).- Ueber die Kapazitaet ebener Kontinuen , Math. Ann. 139 ( 1959), pp. 64-75. | MR | Zbl
[Po2] Padé approximants and convergence in capacity, J. Math. Anal. Appl. 41 (1973), pp. 775-780. | MR | Zbl
-[Ra] On the convergence of Padé approximants in classes of holomorphic functions, Math. USSR Sb. 40 (1980), pp. 149-155. | Zbl
-[Si] Transzendente Zahlen, Bibliographisches Institut, Mannheim ( 1967). | MR | Zbl
-[Sp] Introduction to Riemann Surfaces , Chelsea publ. cop. New York (1981 ). | Zbl
-[St1] Extremal domains associated with an analytic function I, II, Complex Variables Theory Appl. 4 (1985), pp. 311-324, 325-338. | MR | Zbl
-[St2] The structure of extremal domains associated with an analytic function, Complex Variables Theory Appl. 4 (1985), pp. 339-354. | MR | Zbl
-[St3] The convergence of Padé approximants to functions with branch points, Submitted to J. Approx. Theory. | MR | Zbl
-[Sti] Recherches sur les fractions continues , Ann. Fac. Sci. Toulouse 8 (1894), pp. 1-122. | JFM | Numdam | MR
-[StTo] General Orthogonal Polynomials , Encycl. Math. Vol. 43, Cambridge University Press, Cambridge, (1992). | MR | Zbl
and -