• 제목/요약/키워드: q-Stirling numbers

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A STUDY OF POLY-BERNOULLI POLYNOMIALS ASSOCIATED WITH HERMITE POLYNOMIALS WITH q-PARAMETER

  • Khan, Waseem A.;Srivastava, Divesh
    • 호남수학학술지
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    • 제41권4호
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    • pp.781-798
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    • 2019
  • This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.

A q-ANALOGUE OF THE GENERALIZED FACTORIAL NUMBERS

  • Song, Seok-Zun;Cheon, Gi-Sang;Jun, Young-Bae;Beasley, Leroy B.
    • 대한수학회지
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    • 제47권3호
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    • pp.645-657
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    • 2010
  • In this paper, more generalized q-factorial coefficients are examined by a natural extension of the q-factorial on a sequence of any numbers. This immediately leads to the notions of the extended q-Stirling numbers of both kinds and the extended q-Lah numbers. All results described in this paper may be reduced to well-known results when we set q = 1 or use special sequences.

A NOTE ON q-ANALOGUE OF POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • Hwang, Kyung Won;Nam, Bo Ryeong;Jung, Nam-Soon
    • Journal of applied mathematics & informatics
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    • 제35권5_6호
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    • pp.611-621
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    • 2017
  • In this paper, we define a q-analogue of the poly-Bernoulli numbers and polynomials which is generalization of the poly Bernoulli numbers and polynomials including q-polylogarithm function. We also give the relations between generalized poly-Bernoulli polynomials. We derive some relations that are connected with the Stirling numbers of second kind. By using special functions, we investigate some symmetric identities involving q-poly-Bernoulli polynomials.

THE STUDY ON GENERALIZED (p, q)-POLY-GENOCCHI POLYNOMIALS WITH VARIABLE a

  • H.Y. LEE
    • Journal of Applied and Pure Mathematics
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    • 제5권3_4호
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    • pp.197-209
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    • 2023
  • In this paper, the generalized (p, q)-poly-Genocchi polynomials with variable a is defined by generalizing it more, and various properties of this polynomial are introduced. To do this, we define a generating function and use the definition to introduce some interesting properties as follows: basic properties, relation between Stirling numbers of the second kind and generalized (p, q)-poly-Genocchi polynomials with variable a and symmetric properties.

NUMERICAL INVESTIGATION OF ZEROS OF THE FULLY q-POLY-EULER NUMBERS AND POLYNOMIALS OF THE SECOND TYPE

  • JUNG YOOG KANG
    • Journal of Applied and Pure Mathematics
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    • 제5권5_6호
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    • pp.375-387
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    • 2023
  • In this paper, we construct a fully modified q-poly-Euler numbers and polynomials of the second type and give some properties. Finally, we investigate the zeros of the fully modified q-poly-Euler numbers and polynomials of the second type by using computer.

A q-ANALOGUE OF QI FORMULA FOR r-DOWLING NUMBERS

  • Cillar, Joy Antonette D.;Corcino, Roberto B.
    • 대한수학회논문집
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    • 제35권1호
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    • pp.21-41
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    • 2020
  • In this paper, we establish an explicit formula for r-Dowling numbers in terms of r-Whitney Lah and r-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the q, r-Dowling numbers, q, r-Whitney Lah numbers and q, r-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for q, r-Dowling numbers expressed in terms of q, r-Whitney Lah numbers and q, r-Whitney numbers of the second kind.

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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    • 제32권3_4호
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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.

A NOTE ON THE GENERALIZED BERNOULLI POLYNOMIALS WITH (p, q)-POLYLOGARITHM FUNCTION

  • JUNG, N.S.
    • Journal of applied mathematics & informatics
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    • 제38권1_2호
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    • pp.145-157
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    • 2020
  • In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

ON THE (p, q)-POLY-KOROBOV POLYNOMIALS AND RELATED POLYNOMIALS

  • KURT, BURAK;KURT, VELI
    • Journal of applied mathematics & informatics
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    • 제39권1_2호
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    • pp.45-56
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    • 2021
  • D.S. Kim et al. [9] considered some identities and relations for Korobov type numbers and polynomials. In this work, we investigate the degenerate Korobov type Changhee polynomials and the (p,q)-poly-Korobov polynomials. We give a generalization of the Korobov type Changhee polynomials and the (p,q) poly-Korobov polynomials. We prove some properties and identities and explicit relations for these polynomials.