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Mat. Zametki, 2005, Volume 77, Issue 5, Pages 683–706 (Mi mz2536)  

This article is cited in 11 scientific papers (total in 11 papers)

Expansion of Multiple Integrals in Linear Forms

S. A. Zlobin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We prove general theorems on expansions of multiple integrals in linear forms in generalized polylogarithms with coefficients that are rational functions.

DOI: https://doi.org/10.4213/mzm2536

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English version:
Mathematical Notes, 2005, 77:5, 630–652

Bibliographic databases:

UDC: 511+517.5
Received: 08.12.2003
Revised: 13.10.2004

Citation: S. A. Zlobin, “Expansion of Multiple Integrals in Linear Forms”, Mat. Zametki, 77:5 (2005), 683–706; Math. Notes, 77:5 (2005), 630–652

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Kh. Salikhov, A. I. Frolovichev, “On multiple integrals represented as a linear form in $1,\zeta(3),\zeta(5),…,\zeta(2k-1)$”, J. Math. Sci., 146:2 (2007), 5731–5758  mathnet  crossref  mathscinet  zmath
    2. S. A. Zlobin, “Properties of coefficients of certain linear forms in generalized polylogarithms”, J. Math. Sci., 146:2 (2007), 5655–5668  mathnet  crossref  mathscinet  zmath  elib
    3. S. A. Zlobin, “Rhin Integrals”, Math. Notes, 81:2 (2007), 201–212  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Kalmykov M. Yu., Warda B. F. L., Yost S. A., “Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order epsilon-expansion of generalized hypergeometric functions with one half-integer value of parameter”, JHEP, 2007, no. 10, 048  crossref  mathscinet  isi  scopus  scopus
    5. Fischler S., “Multiple series connected to Hoffman's conjecture on multiple zeta values”, J. Algebra, 320:4 (2008), 1682–1703  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. Cresson J., Fischler S., Rivoal T., “Symmetry phenomenon used in polyzeta linear forms”, J. Reine Angew. Math., 617 (2008), 109–151  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Cresson P., Fischler S., Rivoal T., “Séries hypergéométriques multiples et polyzêtas [Multiple hypergeometric series and polyzetas]”, Bull. Soc. Math. France, 136:1 (2008), 97–145  crossref  mathscinet  zmath  isi  elib  scopus
    8. Ohno Ya., Zudilin W., “Zeta stars”, Communications in Number Theory and Physics, 2:2 (2008), 325–347  crossref  mathscinet  zmath  isi  scopus
    9. S. A. Zlobin, “Special values of generalized polylogarithms”, J. Math. Sci., 182:4 (2012), 484–504  mathnet  crossref  mathscinet
    10. Igarashi M., “A Generalization of Ohno's Relation for Multiple Zeta Values”, J. Number Theory, 132:4 (2012), 565–578  crossref  mathscinet  zmath  isi  elib  scopus
    11. Androsenko V.A., “Ob otsenkakh lineinykh form ot chisel 1,”, Vestnik bryanskogo gosudarstvennogo universiteta, 4:4 (2012), 20–27  elib
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