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Algorithms of Integral Representation of Combinatorial Sums and Their Applications

In: Formal Power Series and Algebraic Combinatorics

Author

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  • G. P. Egorychev

    (Krasnoyarsk State Technical University, Chair of Software of Discrete Apparatus and Systems)

Abstract

This article contains investigations on the problem of finding integral representation and computation finite and infinite sums (generating functions) arising in practice in combinatorial analysis, the theory of algorithms and computer algebra, probability theory, group theory, function theory, and so on, as well as in physics and other areas of knowledge. Using the concept “res” (formal residue) and its properties this approach has been extended on sums which supposed a computation in algebra of formal power series of one and several variables over field of real and complex numbers (method of coefficients). Various applications of this method, the list of new problems and some perspectives in further investigations are pointed.

Suggested Citation

  • G. P. Egorychev, 2000. "Algorithms of Integral Representation of Combinatorial Sums and Their Applications," Springer Books, in: Daniel Krob & Alexander A. Mikhalev & Alexander V. Mikhalev (ed.), Formal Power Series and Algebraic Combinatorics, pages 15-29, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04166-6_2
    DOI: 10.1007/978-3-662-04166-6_2
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