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In [1] a number of some combinatorial identities was obtained. 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 C, in particular, of a bicircular domain in C. Similar identities were obtained in [11], where holomorphic monomials were integrated along the boundary of a 3-circular domain in C. These identities were verified and generalized by the method of Egorychev from [12] developed in [13]. The domains considered in [1] and [11] were not complete and the identities obtained have binomial and polynomial coefficients. The structure of the integral representation [14] and known examples imply the following conjecture

Method for Obtaining Combinatorial Identities with Polynomial Coefficients by Means of Integral Representations