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A generalization of the inversion formulas of systems of power series in systems of implicit functions. (English) Zbl 0404.32001


MSC:

32A05 Power series, series of functions of several complex variables

Citations:

Zbl 0369.32001
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References:

[1] A. Cayley, ?Note sur une formule pour la reversion des séries,? J. Reine Angew. Math.,52, 276-284 (1856). · ERAM 052.1380cj · doi:10.1515/crll.1856.52.276
[2] J. J. Sylvester, ?On the change of systems of independent variables,? Q. J. Math.,1, 43-56, 126-134 (1857).
[3] R. A. Sack, ?Generalization of Lagrange’s expansion for functions of several implicitly defined variables,? J. Soc. Ind. App. Math.,134, 913-926 (1965). · Zbl 0143.27403 · doi:10.1137/0113059
[4] G. G. Jacobi, ?De resolutione aequationum per series infinitas,? J. Reine Angew. Math.,6, 257-286 (1830). · ERAM 006.0240cj · doi:10.1515/crll.1830.6.257
[5] A. P. Yuzhakov and A. V. Kuprikov, ?On the logarithmic residue in Cn,? in: Properties of Holomorphic Functions of Several Complex Variables [in Russian], Izd. Inst. Fiz. Sib. Otd. Akad. Nauk SSSR (1973), pp. 181-191.
[6] A. P. Yuzhakov, ?On the application of the multiple logarithmic residue to expansion of implicit functions in power series,? Mat. Sb.,97, No. 2, 177-192 (1975). · Zbl 0326.32002
[7] B. V. Shabat, Introduction to Complex Analysis [in Russian], Nauka, Moscow (1969). · Zbl 0188.37902
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