Mathematics & Physics 2016, 9(2), 192–201 УДК 517.55+519.1 Method for Obtaining Combinatorial Identities with Polynomial Coefficients by Means of Integral Representations Viacheslav P. Krivokolesko∗ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 06.12.2015, received in revised form 08.01.2016, accepted 12.02.2016 We propose a method how to derive combinatorial identities with polynomial coefficients by means of an integral representation of holomorphic functions in an n-circular linearly convex polyhedron. <...> One of such identities is a generalization of the Chaundy-Bullard identity [2], see also [3–10] The proof was based on integration of holomorphic monomials along a piecewise regular boundary of a bounded linearly convex n-circular domain in Cn, in particular, of a bicircular domain in C2. <...> Similar identities were obtained in [11], where holomorphic monomials were integrated along the boundary of a 3-circular domain in C3. <...> These identities were verified and generalized by the method of Egorychev from [12] developed in [13]. <...> The integral representation in [14] permits one to obtain combinatorial identities related to the geometry of a domain, along whose boundary the integration of a holomorphic function is performed. <...> As follows from the proof of theorem 6 of this paper, this conjecture is proved to be true for complete bounded linearly convex domains with piecewise regular boundary in Cn. The article consists of three sections, the first two preceed the proof of the main theorem. <...> In the first section we formulate the theorem on the integral representation in bounded n-circular linearly convex domains with piecewise regular boundary in Cn and introduce the necessary notation and definitions. <...> In the last section we formulate and prove a lemma and the main theorem. ∗krivokolesko@gmail.com ⃝ Siberian Federal University. <...> All rights reserved c – 192 – +, where Rn + is Viacheslav P. Krivokolesko Method for Obtaining Combinatorial Identities with Polynomial Coefficients . . . 1. <...> Integral representation in n-circular linearly convex domains with piecewise regular boundary in Cn there is a complex (n−1)-dimensional analytic plane passing through the point z0 and disjoint from G (note that some authors use the term "weak linear convexity", for example, see [16]). <...> A domain G ⊂ Cn is called linearly convex ( [15], §8 <...>