• Title, Summary, Keyword: Stirling number of the first kind

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SIMPLIFYING AND FINDING ORDINARY DIFFERENTIAL EQUATIONS IN TERMS OF THE STIRLING NUMBERS

  • Qi, Feng;Wang, Jing-Lin;Guo, Bai-Ni
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.675-681
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    • 2018
  • In the paper, by virtue of techniques in combinatorial analysis, the authors simplify three families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind and establish a new family of nonlinear ordinary differential equations in terms of the Stirling numbers of the second kind.

OME PROPERTIES OF THE BERNOULLI NUMBERS OF THE SECOND KIND AND THEIR GENERATING FUNCTION

  • Qi, Feng;Zhao, Jiao-Lian
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1909-1920
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    • 2018
  • In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

A STUDY OF SUM OF DIVISOR FUNCTIONS AND STIRLING NUMBER OF THE FIRST KIND DERIVED FROM LIOUVILLE FUNCTIONS

  • KIM, DAEYEOUL;KIM, SO EUN;SO, JI SUK
    • Journal of applied mathematics & informatics
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    • v.36 no.5_6
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    • pp.435-446
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    • 2018
  • Using the theory of combinatoric convolution sums, we establish some arithmetic identities involving Liouville functions and restricted divisor functions. We also prove some relations involving restricted divisor functions and Stirling numbers of the first kind for divisor functions.

EXPLICIT EVALUATION OF HARMONIC SUMS

  • Xu, Ce
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.13-36
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    • 2018
  • In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several quadratic and cubic Euler sums through zeta values and linear sums. Furthermore, some relationships between harmonic numbers and Stirling numbers of the first kind are established.

AN EXTENSION OF GENERALIZED EULER POLYNOMIALS OF THE SECOND KIND

  • Kim, Y.H.;Jung, H.Y.;Ryoo, C.S.
    • Journal of applied mathematics & informatics
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    • v.32 no.3_4
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    • pp.465-474
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    • 2014
  • Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.