• 제목/요약/키워드: Multiple Polynomials

검색결과 52건 처리시간 0.017초

SOME RECURRENCE RELATIONS OF MULTIPLE ORTHOGONAL POLYNOMIALS

  • Lee, Dong-Won
    • 대한수학회지
    • /
    • 제42권4호
    • /
    • pp.673-693
    • /
    • 2005
  • In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures $(d{\mu},\;dv)$ and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case.

A DIFFERENTIAL EQUATION FOR MULTIPLE BESSEL POLYNOMIALS WITH RAISING AND LOWERING OPERATORS

  • Baek, Jin-Ok;Lee, Dong-Won
    • 대한수학회보
    • /
    • 제48권3호
    • /
    • pp.445-454
    • /
    • 2011
  • In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

Multiple Weakly Summing Multilinear Mappings and Polynomials

  • Kim, Sung Guen
    • Kyungpook Mathematical Journal
    • /
    • 제47권4호
    • /
    • pp.501-517
    • /
    • 2007
  • In this paper, we introduce and study a new class containing absolutely summing multilinear mappings and polynomials, which we call multiple weakly summing multilinear mappings and polynomials. We investigate some interesting properties about multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials defined on Banach spaces: In particular, we prove a kind of Dvoretzky-Rogers' Theorem and an ideal property for multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials. We also prove that the Aron-Berner extensions of multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing multilinear mappings and polynomials are also multiple weakly ($p$; $q_1$, ${\cdots}$, $q_k$)-summing.

  • PDF

ON THE SPECIAL VALUES OF TORNHEIM'S MULTIPLE SERIES

  • KIM, MIN-SOO
    • Journal of applied mathematics & informatics
    • /
    • 제33권3_4호
    • /
    • pp.305-315
    • /
    • 2015
  • Recently, Jianxin Liu, Hao Pan and Yong Zhang in [On the integral of the product of the Appell polynomials, Integral Transforms Spec. Funct. 25 (2014), no. 9, 680-685] established an explicit formula for the integral of the product of several Appell polynomials. Their work generalizes all the known results by previous authors on the integral of the product of Bernoulli and Euler polynomials. In this note, by using a special case of their formula for Euler polynomials, we shall provide several reciprocity relations between the special values of Tornheim's multiple series.

A DIFFERENCE EQUATION FOR MULTIPLE KRAVCHUK POLYNOMIALS

  • Lee, Dong-Won
    • 대한수학회지
    • /
    • 제44권6호
    • /
    • pp.1429-1440
    • /
    • 2007
  • Let ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ as solutions. Lastly we give an explicit difference equation for ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ for the case of r=2.

STRUCTURE RELATIONS OF CLASSICAL MULTIPLE ORTHOGONAL POLYNOMIALS BY A GENERATING FUNCTION

  • Lee, Dong Won
    • 대한수학회지
    • /
    • 제50권5호
    • /
    • pp.1067-1082
    • /
    • 2013
  • In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

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

  • KURT, BURAK;KURT, VELI
    • Journal of applied mathematics & informatics
    • /
    • 제39권1_2호
    • /
    • pp.45-56
    • /
    • 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.

ON CERTAIN MULTIPLES OF LITTLEWOOD AND NEWMAN POLYNOMIALS

  • Drungilas, Paulius;Jankauskas, Jonas;Junevicius, Grintas;Klebonas, Lukas;Siurys, Jonas
    • 대한수학회보
    • /
    • 제55권5호
    • /
    • pp.1491-1501
    • /
    • 2018
  • Polynomials with all the coefficients in {0, 1} and constant term 1 are called Newman polynomials, whereas polynomials with all the coefficients in {-1, 1} are called Littlewood polynomials. By exploiting an algorithm developed earlier, we determine the set of Littlewood polynomials of degree at most 12 which divide Newman polynomials. Moreover, we show that every Newman quadrinomial $X^a+X^b+X^c+1$, 15 > a > b > c > 0, has a Littlewood multiple of smallest possible degree which can be as large as 32765.