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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 1, Pages 69–122 (Mi izv1815)  

This article is cited in 5 scientific papers (total in 6 papers)

Classes of formulas and expansions of Taylor–Maclaurin type associated with differential operators of fractional order

M. M. Dzhrbashyan, B. A. Saakyan


Abstract: This article contains new applications of functions of Mittag–Leffler type $E_\rho(z,\mu)=\sum_0^\infty\Gamma^{-1}(\mu+\frac k\rho)z^k$ in mathematical analysis. We construct an apparatus of formulas and expansions of Taylor–Maclaurin type in systems generated by a system of functions of the form $\{E_\rho(-\lambda_nx^{1/\rho},\frac1\rho)\}_0^\infty$ and an arbitrary sequence $\{\lambda_n\}_0^\infty$ ($0=\lambda_0\leqslant\lambda_n\leqslant\lambda_{n+1}$). In addition, in the article we introduce essentially new classes $\langle\rho,\lambda_n\rangle$ of absolutely monotone functions and establish theorems on their representations.
Bibliography: 9 items.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:1, 63–112

Bibliographic databases:

UDC: 517.5
MSC: Primary 26A33; Secondary 26A93, 26A48, 30A16, 30A78
Received: 22.11.1973

Citation: M. M. Dzhrbashyan, B. A. Saakyan, “Classes of formulas and expansions of Taylor–Maclaurin type associated with differential operators of fractional order”, Izv. Akad. Nauk SSSR Ser. Mat., 39:1 (1975), 69–122; Math. USSR-Izv., 9:1 (1975), 63–112

Citation in format AMSBIB
\Bibitem{DzhSah75}
\by M.~M.~Dzhrbashyan, B.~A.~Saakyan
\paper Classes of formulas and expansions of Taylor--Maclaurin type associated with differential operators of fractional order
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 1
\pages 69--122
\mathnet{http://mi.mathnet.ru/izv1815}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=372130}
\zmath{https://zbmath.org/?q=an:0323.33005}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 1
\pages 63--112
\crossref{https://doi.org/10.1070/IM1975v009n01ABEH001473}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. U. Arakelian, A. G. Vitushkin, V. S. Vladimirov, A. A. Gonchar, “Mkhitar Mkrtichevich Dzhrbashyan (on his sixtieth birthday)”, Russian Math. Surveys, 34:2 (1979), 269–275  mathnet  crossref  mathscinet  zmath
    2. B. A. Sahakyan, “On the solutions of some differential equations of fractional order in complex domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2010, no. 3, 29–34  mathnet
    3. B. A. Sahakyan, “Classes of Taylor–Maclourin type formulae in complex domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2011, no. 2, 3–10  mathnet
    4. B. A. Sahakyan, “General classes of TaylorMaclaurin type formulas in complex domain”, Uch. zapiski EGU, ser. Fizika i Matematika, 2012, no. 1, 20–26  mathnet
    5. B. A. Sahakyan, “On the representation of $\langle\rho_j, W_j\rangle$ absolute monotone functions”, Uch. zapiski EGU, ser. Fizika i Matematika, 2014, no. 1, 26–34  mathnet
    6. B. A. Sahakyan, “On a generalized formula of TaylorMaclaurin type on the generalized completely monotone functions”, Uch. zapiski EGU, ser. Fizika i Matematika, 52:3 (2018), 172–179  mathnet
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