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On the Weierstrass functions, sigma, zeta, pe, and their functional and differential equations. (English) Zbl 0378.33005


MSC:

33C60 Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions)
34M99 Ordinary differential equations in the complex domain
39B05 General theory of functional equations and inequalities
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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References:

[1] Hayman, W. K.,Meromorphic Functions. Oxford, Clarendon Press, London (1964).
[2] Miles, J. Quotient representations of meromorphic functions. J. Analyse Math.25 (1972), 371–388. · Zbl 0247.30019 · doi:10.1007/BF02790046
[3] Nevanlinna, R.,Le Théorème de Picard-Borel et La Théorie des Fonctions Méromorphes. Gauthier-Villars, Paris, 1929.
[4] Rellich, F.,Elliptsche Funktionen und die ganzen Lösungen von y”=f(y). Math. Z.47 (1942), 153–160. · JFM 66.0396.03 · doi:10.1007/BF01180954
[5] Saks, S. andZygmund, A.,Analytic Functions. Monografie Mat. Vol. 28, Warsaw, 1952.
[6] Tsuji, M.,Potential Theory in Modern Function Theory. Maruzen Co., Tokyo, 1959. · Zbl 0087.28401
[7] Valiron, G.,Fonctions Analytiques. Presses Universitaires de France, Paris, 1954.
[8] Wittich, H.,Neure Untersuchungen über eindeutige analytische Fonctionen. Ergebnisse der Mathematik, Heft 8, Springer-Verlag, Berlin, 1955. · Zbl 0067.05501
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