Integer properties of a composition of exponential generating functions

Dmitry V. Kruchinin, Yuriy V. Shablya, Oleg O. Evsutin, Alexander A. Shelupanov

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite numbers. Using the results of the paper we get the known properties of the Bell numbers (Touchard's Congruence for k = 0).

    Original languageEnglish
    Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016
    PublisherAmerican Institute of Physics Inc.
    Volume1863
    ISBN (Electronic)9780735415386
    DOIs
    Publication statusPublished - 21 Jul 2017
    EventInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016 - Rhodes, Greece
    Duration: 19 Sep 201625 Sep 2016

    Conference

    ConferenceInternational Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016
    CountryGreece
    CityRhodes
    Period19.9.1625.9.16

    Fingerprint

    exponential functions
    integers
    congruences
    bells
    composite materials

    Keywords

    • composition of generating function
    • exponential generating function
    • prime

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    Kruchinin, D. V., Shablya, Y. V., Evsutin, O. O., & Shelupanov, A. A. (2017). Integer properties of a composition of exponential generating functions. In International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016 (Vol. 1863). [300014] American Institute of Physics Inc.. https://doi.org/10.1063/1.4992463

    Integer properties of a composition of exponential generating functions. / Kruchinin, Dmitry V.; Shablya, Yuriy V.; Evsutin, Oleg O.; Shelupanov, Alexander A.

    International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016. Vol. 1863 American Institute of Physics Inc., 2017. 300014.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Kruchinin, DV, Shablya, YV, Evsutin, OO & Shelupanov, AA 2017, Integer properties of a composition of exponential generating functions. in International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016. vol. 1863, 300014, American Institute of Physics Inc., International Conference of Numerical Analysis and Applied Mathematics 2016, ICNAAM 2016, Rhodes, Greece, 19.9.16. https://doi.org/10.1063/1.4992463
    Kruchinin DV, Shablya YV, Evsutin OO, Shelupanov AA. Integer properties of a composition of exponential generating functions. In International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016. Vol. 1863. American Institute of Physics Inc. 2017. 300014 https://doi.org/10.1063/1.4992463
    Kruchinin, Dmitry V. ; Shablya, Yuriy V. ; Evsutin, Oleg O. ; Shelupanov, Alexander A. / Integer properties of a composition of exponential generating functions. International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2016. Vol. 1863 American Institute of Physics Inc., 2017.
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