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Khristo N. Boyadzhiev

  1. Eratosthenes and Pliny, Greek geometry and Roman follies.

    Tue, 06/15/2010 - 15:01 — SomNambul
    Authors: Khristo N. Boyadzhiev
    Subjects: History and Overview
    Abstract

    Supportive attitudes can bring to a blossoming science, while neglect can
    quickly make science absent from everyday life and provide a very primitive
    view of the world. We compare one important Greek achievement, the computation
    of the earth meridian by Eratosthenes, to its later interpretation by the Roman
    historian of science Pliny.

  2. Series with Hermite Polynomials and Harmonic Numbers.

    Tue, 06/15/2010 - 15:01 — SomNambul
    Authors: Khristo N. Boyadzhiev
    Subjects: Number Theory
    Abstract

    We obtain a series transformation formula involving the classical Hermite
    polynomials. We then provide a number of applications using appropriate
    binomial transformations. Several of the new series involve Hermite polynomials
    and Harmonic numbers. We also obtain a series involving both Hermite and
    Laguerre polynomials, and a series with Hermite polynomials and Stirling
    numbers of the second kind.

  3. Evaluation of some simple Euler-type series.

    Thu, 12/17/2009 - 16:01 — SomNambul
    Authors: Khristo N. Boyadzhiev
    Subjects: Number Theory
    Abstract

    Five series are evaluated in terms of zeta values. Three of the series
    involve harmonic numbers and one involves Stirling numbers of the first kind.
    The evaluation of these series is reduced to the evaluation of certain
    integrals, including the moments of the polylogarithm.

  4. Power sum identities with generalized Stirling numbers.

    Fri, 09/11/2009 - 19:12 — SomNambul
    Authors: Khristo N. Boyadzhiev
    Subjects: Combinatorics
    Abstract

    Several combinatorial identities are presented, involving Stirling functions
    of the second kind with a complex variable. The identities involve also
    Stirling numbers of the first kind, binomial coefficients and harmonic numbers.

  5. Exponential Polynomials, Stirling Numbers,and Evaluation of Some Gamma Integrals.

    Tue, 09/08/2009 - 12:16 — SomNambul
    Authors: Khristo N. Boyadzhiev
    Subjects: Classical Analysis and ODEs
    Abstract

    This article is a survey of the exponential polynomials (also called
    single-variable Bell polynomials) from the point of view of Analysis. Some new
    properties are included and several Analysis-related applications are
    mentioned.

  6. Exponential Polynomials, Stirling Numbers,and Evaluation of Some Gamma Integrals.

    Tue, 09/08/2009 - 12:16 — SomNambul
    Authors: Khristo N. Boyadzhiev
    Subjects: Classical Analysis and ODEs
    Abstract

    This article is a survey of the exponential polynomials (also called
    single-variable Bell polynomials) from the point of view of Analysis. Some new
    properties are included and several Analysis-related applications are
    mentioned.

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