Method for obtaining combinatorial identities with polynomial coefficients by means of integral representations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 192-201.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: combinatorial identities, integral representation.
Mots-clés : polynomial coefficients
@article{JSFU_2016_9_2_a7,
     author = {Viacheslav P. Krivokolesko},
     title = {Method for obtaining combinatorial identities with polynomial coefficients by means of integral representations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {192--201},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a7/}
}
TY  - JOUR
AU  - Viacheslav P. Krivokolesko
TI  - Method for obtaining combinatorial identities with polynomial coefficients by means of integral representations
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2016
SP  - 192
EP  - 201
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a7/
LA  - en
ID  - JSFU_2016_9_2_a7
ER  - 
%0 Journal Article
%A Viacheslav P. Krivokolesko
%T Method for obtaining combinatorial identities with polynomial coefficients by means of integral representations
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2016
%P 192-201
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a7/
%G en
%F JSFU_2016_9_2_a7
Viacheslav P. Krivokolesko. Method for obtaining combinatorial identities with polynomial coefficients by means of integral representations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 2, pp. 192-201. http://geodesic.mathdoc.fr/item/JSFU_2016_9_2_a7/

[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] T. W. Chaundy, J. E. Bullard, “John Smith's problem”, Math. Gazette, 44 (1960), 253–260 | DOI | Zbl

[3] V. M. Shelkovich, “Algebra of distributions with a point singular support”, Dokl. AN SSSR, 267:1 (1982), 53–57 (in Russian) | MR | Zbl

[4] I. Daubeacheis, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992 | MR

[5] D. Zielberger, “On an identity of Daubeachies”, Amer. Math. Monthly, 100 (1993), 487 | DOI | MR

[6] T. H. Koornwinder, M. J. Schlosser, “On an identity Chaundy and Bullard, I”, Indag. Math. (N.S), 19 (2008), 239–261 | DOI | MR | Zbl

[7] G. P. Egorychev, “Combinatorial identity from the theory of integral representations in $\mathbb{C}^{n}$”, Irkutsk Gos. Univ. Mat., 4:4 (2011), 32–44 (in Russian)

[8] V. P. Krivokolesko, E. K. Leinartas, “On identities with polynomial coefficients”, Irkutsk Gos. Univ. Mat., 5:3 (2012), 56–63 (in Russian)

[9] T. H. Koornwinder, M. J. Schlosser, “On an identity Chaundy and Bullard, II”, More history, Indag. Math. (N.S), 24 (2013), 174–180 | DOI | MR | Zbl

[10] H. Alzer, “On a combiatorial sum”, Indag. Math., 26 (2015), 519–525 | DOI | MR | Zbl

[11] V. P. Krivokolesko, “Integral representation of holomophic functions in n-circular linear convex domain with piecewise regular boudary”, Mat. sistemy, 10, Izd. KrasGAU, Krasnoyarsk, 2011, 95–107 (in Russian)

[12] G.P. Egorychev, Integral Representation and the Computation of Combinatorial Sums, Trans. of Math. Monogr., 59, Amer. Math. Soc., Providence, RI, 1984 | MR | Zbl

[13] M. N. Davletshin, G. P. Egorychev, V. P. Krivokolesko, “Calculation of multiple combinatorial sums in the theory of holomorphic functions in $\mathbb C^{n}$”, Advances in Applied Mathematics, 48 (2012), 446–456 | DOI | MR | Zbl

[14] V. P. Krivokolesko, A. K. Tsikh, “Integral representations in linearly convex polyhedra”, Sib. Mat. J., 46:3 (2005), 579–593 | MR | Zbl

[15] L. A. Aizenberg, A. P. Yuzhakov, Integral Represetations and Residues in Multidimensional Complex Analysis, AMS, RI, Providence, 1983

[16] M. Andersson, M. Passare, R. Sigurdsson, Complex convexity and analytic functionals, Progr. Math., 225, Birkhäuser, Basel–Boston–Berlin, 2004 | MR | Zbl

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