Diagonal Padé approximants to hyperelliptic functions
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, 100 ans après Th.-J. Stieltjes - Numéro spécial, Tome S5 (1996), pp. 121-193. 
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     author = {Stahl, Herbert},
     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},
     mrnumber = {1462709},
     zbl = {0872.41006},
     language = {en},
     url = {http://www.numdam.org/item/AFST_1996_6_S5__121_0/}
}
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Stahl, Herbert. Diagonal Padé approximants to hyperelliptic functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, 100 ans après Th.-J. Stieltjes - Numéro spécial, Tome S5 (1996), pp. 121-193. http://www.numdam.org/item/AFST_1996_6_S5__121_0/

[BaGM] Baker ( G.A.) JR. and Graves-Morris . - Padé Approximants Parts I and Part II, Encycl. Math. Vols 13 and 14. Cambridge University Press, Cambridge (1981).

[BGW] Baker (G. A.) Jr., Gammel (J.L.) and Wills (J.G.).- An investigation of the applicability of the Padé approximant method, J. Math. Anal. Appl. 2 (1961), pp. 405-418. | MR | Zbl

[Br] Brezinsk I ( C.). - History of Continued Fractions and Padé approximants, Series in Comp. Math. 12, Springer-Verlag, Heidelberg (1991). | MR | Zbl

[Bo] Borchardt ( C.W.).- Application des transcendantes abéliennes á la théorie des fractions continues, J. Reine Angew. Math. 48 (1854), pp. 69-104. | Zbl

[Ch] Chandrasehharan ( K.).- Analytic Number Theory, Springer-Verlag, Berlin ( 1968).

[Du] Dumas (S. ).- Sur le développement des fonctions elliptiques en fractions continues, Thésis, Univ. Zürich, (1908). | JFM

[Go] Gonchar ( A.A.).- 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] Gonchar ( A.A.) and Rakhmanov (E.A.).- 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

[Ham] Hamburger ( H.).- 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] Halphen (G.-H. ).- Traité des fonctions elliptiques et de leurs applications, Tome II. Gauthier-Villars, Paris ( 1888). | JFM

[Hi] Hille (E.). - Analytic Function Theory, Ginns and Company, Boston (1962). | MR

[HuCo] Hurwitz (A. ) and Courant ( R.).- Funktionentheorie, Springer-Verlag, Berlin ( 1929).

[Ja] Jacobi (C.-G.-J. ).- 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] Krein (M.G. ). - 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] Landkof (N.S. ).- Foundations of Modern Potential Theory , Springer-Verlag Berlin (1972). | MR | Zbl

[Lu] Lubinsky ( D.S.). - Divergence of complex rational approximants , Pacific J. Math. 108 (1983), pp. 141-153. | MR | Zbl

[Nu1] Nuttall ( J.).- The convergence of Padé approximants of meromorphic functions, J. Math. Anal. Appl. 31 (1970), pp. 129-140. | MR | Zbl

[Nu2] Nuttall ( J.).- Asymptotics of diagonal Hermite-Padé polynomials, J. Approx. Theory 42 (1984), pp. 299-386. | MR | Zbl

[Pe] Perron (O.). - 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] Pommerenke ( Ch. ).- Padé approximants and convergence in capacity, J. Math. Anal. Appl. 41 (1973), pp. 775-780. | MR | Zbl

[Ra] Rakhmanov ( E.A.).- On the convergence of Padé approximants in classes of holomorphic functions, Math. USSR Sb. 40 (1980), pp. 149-155. | Zbl

[Si] Siegel (C.L. ). - Transzendente Zahlen, Bibliographisches Institut, Mannheim ( 1967). | MR | Zbl

[Sp] Springer (G. ). - Introduction to Riemann Surfaces , Chelsea publ. cop. New York (1981 ). | Zbl

[St1] Stahl (H. ).- Extremal domains associated with an analytic function I, II, Complex Variables Theory Appl. 4 (1985), pp. 311-324, 325-338. | MR | Zbl

[St2] Stahl (H. ).- The structure of extremal domains associated with an analytic function, Complex Variables Theory Appl. 4 (1985), pp. 339-354. | MR | Zbl

[St3] Stahl (H. ).- The convergence of Padé approximants to functions with branch points, Submitted to J. Approx. Theory. | MR | Zbl

[Sti] Stieltjes ( T.-J.).- Recherches sur les fractions continues , Ann. Fac. Sci. Toulouse 8 (1894), pp. 1-122. | JFM | Numdam | MR

[StTo] Stahl ( H.) and Totik (V.).- General Orthogonal Polynomials , Encycl. Math. Vol. 43, Cambridge University Press, Cambridge, (1992). | MR | Zbl