Literature Cited
G. P. Egorychev, “Method of classifying and obtaining numerical identities of combinatorial analysis,” in: Algebra [in Russian], In-t Fiziki SO AN SSSR, Krasnoyarsk (1970), pp. 94–115.
G. P. Egorychev, “The correlation between symbolic methods of combinatorial analysis and the apparatus of generating functions,” in: Algebra [in Russian], In-t Fiziki SO AN SSSR, Krasnoyarsk (1970), pp. 116–130.
G. P. Egorychev and A. P. Yuzhakov, “The application of multidimensional residues to the determination of generating functions and the computation of combinatorial sums,” in: Holomorphic Functions of Several Complex Variables [in Russian], In-t Fiziki SO AN SSSR, Krasnoyarsk (1972), pp. 47–61.
M. Hall, Combinatorial Analysis [Russian translation], IL, Moscow (1963).
I. J. Good, “Generalization to several variables of Lagrange's expansion,” Proc. Cambridge Phil. Soc.,56, No. 4, 367–380 (1960).
I. J. Good, “A short proof of MacMahon's ‘Master Theorem’,” Proc. Cambridge Phil. Soc.,58, 160 (1962).
J. Percus, Combinatorial Methods, Springer, New York (1971).
Z. Govindarajulu and Y. Suziki, “A note on an identity involving binomial coefficients,” Ann. Inst. Statist. Math.,15, No. 1, 83–85 (1963).
O. V. Sarmanov, B. A. Sevanst'yanov, and V. E. Tarakanov, “Some combinatorial identities,” Matem. Zametki,11, No. 1, 121–127 (1972).
B. V. Shabat, Introduction to Complex Analysis [in Russian], Nauka (1969).
J. Milnor, Singular Points of Complex Hypersurfaces, Princeton University Press, Princeton (1968).
R. Narasimkhan, Analysis on Real and Complex Manifolds [in Russian], Mir, Moscow (1971).
A. P. Yuzhakov, “Residues of functions of several variables,” Izv. Vyssh. Uchebn. Zavedenii, Matematika,5, 149–161 (1964).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 15, No. 5, pp. 1049–1060, September–October, 1974.
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Egorychev, G.P., Yuzhakov, A.P. The determination of generating functions and combinatorial sums by multidimensional residues. Sib Math J 15, 740–747 (1974). https://doi.org/10.1007/BF00966434
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DOI: https://doi.org/10.1007/BF00966434