• Title/Summary/Keyword: (p, q)-numbers

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NEW THEOREM ON SYMMETRIC FUNCTIONS AND THEIR APPLICATIONS ON SOME (p, q)-NUMBERS

  • SABA, N.;BOUSSAYOUD, A.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.243-257
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    • 2022
  • In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.

A NUMERICAL INVESTIGATION ON THE STRUCTURE OF THE ROOT OF THE (p, q)-ANALOGUE OF BERNOULLI POLYNOMIALS

  • Ryoo, Cheon Seoung
    • Journal of applied mathematics & informatics
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    • v.35 no.5_6
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    • pp.587-597
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    • 2017
  • In this paper we define the (p, q)-analogue of Bernoulli numbers and polynomials by generalizing the Bernoulli numbers and polynomials, Carlitz's type q-Bernoulli numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Bernoulli numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Bernoulli polynomials by using computer.

ON THE (p, q)-ANALOGUE OF EULER ZETA FUNCTION

  • RYOO, CHEON SEOUNG
    • Journal of applied mathematics & informatics
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    • v.35 no.3_4
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    • pp.303-311
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    • 2017
  • In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

q-EXTENSIONS OF GENOCCHI NUMBERS

  • CENKCI MEHMET;CAN MUMUN;KURT VELI
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.183-198
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    • 2006
  • In this paper q-extensions of Genocchi numbers are defined and several properties of these numbers are presented. Properties of q-Genocchi numbers and polynomials are used to construct q-extensions of p-adic measures which yield to obtain p-adic interpolation functions for q-Genocchi numbers. As an application, general systems of congruences, including Kummer-type congruences for q-Genocchi numbers are proved.

FULLY MODIFIED (p, q)-POLY-TANGENT POLYNOMIALS WITH TWO VARIABLES

  • N.S. JUNG;C.S. RYOO
    • Journal of applied mathematics & informatics
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    • v.41 no.4
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    • pp.753-763
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    • 2023
  • In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

ON p, q-DIFFERENCE OPERATOR

  • Corcino, Roberto B.;Montero, Charles B.
    • Journal of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.537-547
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    • 2012
  • In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

ON BERNOULLI NUMBERS

  • Kim, Min-Soo;Son, Jin-Woo
    • Journal of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.391-410
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    • 2000
  • In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

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ON A q-ANALOGUE OF THE p-ADIC GENERALIZED TWISTED L-FUNCTIONS AND p-ADIC q-INTEGRALS

  • Lee, Chae-Jang
    • Journal of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.1-10
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    • 2007
  • The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

A NOTE ON (p, q)-ANALOGUE TYPE OF FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS

  • Khan, Waseem A.;Khan, Idrees A.
    • East Asian mathematical journal
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    • v.36 no.1
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    • pp.13-24
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    • 2020
  • The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.