Geodesic
Computation of an integral of a rational function over the skeleton of unit polycylinder in $\mathbb C^{n}$ by means of the Mellin transform
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 364-369 Cet article a éte moissonné depuis la source Math-Net.Ru

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With the help of the Mellin transform we give a simple calculation of an integral of rational functions in several independent parameters aerlier appeared in [2]. The efficiency of this transform is due to the fact that calculation the degree of the polynomial acts as the degree of a monomial. In 2008, G. P. Egorychev and E.V. Zima [5] for the first time successfully used the Mellin transform in the theory of rational summation. The possibility of its application in the analysis and computation of integrals with different types of rational functions is discussed.
Keywords: integral representations, Mellin transform, combinatorial identities. 
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Georgy P. Egorychev; Viachelsav P. Krivokolesko. Computation of an integral of a rational function over the skeleton of unit polycylinder in $\mathbb C^{n}$ by means of the Mellin transform. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 364-369. http://geodesic.mathdoc.fr/item/JSFU_2018_11_3_a12/

[1] V.P. Krivokolesko, “Integral representations for linearly convex polyhedra and some combinatorial identities”, J. Sib. Fed. Univ. Math. Phys., 2:2 (2009), 176–188 (in Russian)

[2] M. Forsberg, M. Passare, A. Tsikh, “Laurent Determinants and Arrangements of Hyperplane Amoebas”, Advances in Mathematics, 151 (2000), 45–70 | DOI | MR | Zbl

[3] V.P. Krivokolesko, “Method for Obtaining Sombinatorial Identities with Polynomial Coefficients by the Means of Integral Representations”, J. Sib. Fed. Univ. Math. Phys., 9:2 (2016), 192–201 | DOI | MR

[4] G.P. Egorychev, Integral representation and the computation of combinatorial sums, Transl. of Math. Monogr., 59, Amer. Math. Soc., Providence, RI, 1984 ; 2-nd Ed., 1989 | DOI | MR | Zbl

[5] G.P. Egorychev, E.V. Zima, Handbook of Algebra, ed. M. Hazewinkel, Elsevier, Integral representation and algorithms for closed form summation | MR