共查询到10条相似文献,搜索用时 125 毫秒
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Christiansen 《Constructive Approximation》2008,19(1):1-22
Abstract. We consider the indeterminate Stieltjes moment problem associated with the q -Laguerre polynomials. A transformation of the set of solutions, which has all the classical solutions as fixed points, is
established and we present a method to construct, for instance, continuous singular solutions. The connection with the moment
problem associated with the Stieltjes—Wigert polynomials is studied; we show how to come from q -Laguerre solutions to Stieltjes—Wigert solutions by letting the parameter α —> ∞ , and we explain how to lift a Stieltjes—Wigert solution to a q -Laguerre solution at the level of Pick functions. Based on two generating functions, expressions for the four entire functions
from the Nevanlinna parametrization are obtained. 相似文献
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M. A. Khan 《Czechoslovak Mathematical Journal》1997,47(4):619-626
The present paper deals with certain generating functions and recurrence relations for q-Laguerre polynomials through the use of the T
k,q,x-operator introduced in an earlier paper [7]. 相似文献
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Christiansen 《Constructive Approximation》2002,19(1):1-22
Abstract. We consider the indeterminate Stieltjes moment problem associated with the q -Laguerre polynomials. A transformation of the set of solutions, which has all the classical solutions as fixed points, is established and we present a method to construct, for instance, continuous singular solutions. The connection with the moment problem associated with the Stieltjes—Wigert polynomials is studied; we show how to come from q -Laguerre solutions to Stieltjes—Wigert solutions by letting the parameter α —> ∞ , and we explain how to lift a Stieltjes—Wigert solution to a q -Laguerre solution at the level of Pick functions. Based on two generating functions, expressions for the four entire functions from the Nevanlinna parametrization are obtained. 相似文献
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In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included. 相似文献
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Two q-difference equations with solutions expressed by q-exponential operator identities are investigated. As applications, two extensions of Ramanujan?s formulas for q-beta integral are given, two generalizations of Andrews–Askey integral are obtained. In addition, generating functions for generalized Al-Salam–Carlitz polynomials are deduced. At last, a generalized transformation identity is gained. 相似文献
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We use the generating functions of some q-orthogonal polynomials to obtain mixed recurrence relations involving polynomials with shifted parameter values. These relations are used to prove interlacing results for the zeros of Al-Salam-Chihara, continuous q-ultraspherical, q-Meixner-Pollaczek and q-Laguerre polynomials of the same or adjacent degree as one of the parameters is shifted by integer values or continuously within a certain range. Numerical examples are given to illustrate situations where the zeros do not interlace. 相似文献
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Jian Cao 《Studies in Applied Mathematics》2013,131(2):105-118
In this paper, generalizations of certain q‐integrals are given by the method of q‐difference equation, which involves the Andrews–Askey integral. In addition, some mixed generating functions for generalized Rogers–Szegö polynomials are obtained by the technique of q‐integral. More over, generating functions for generalized Andrews–Askey polynomials are achieved by q‐integral. 相似文献
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Junesang Choi P.J. Anderson H.M. Srivastava 《Applied mathematics and computation》2009,215(3):1185-1208
In this paper, we systematically recover the identities for the q-eta numbers ηk and the q-eta polynomials ηk(x), presented by Carlitz [L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948) 987–1000], which we define here via generating series rather than via the difference equations of Carlitz. Following a method developed by Kaneko et al. [M. Kaneko, N. Kurokawa, M. Wakayama, A variation of Euler’s approach to the Riemann zeta function, Kyushu J. Math. 57 (2003) 175–192] for a canonical q-extension of the Riemann zeta function, we investigate a similarly constructed q-extension of the Hurwitz zeta function. The details of this investigation disclose some interesting connections among q-eta polynomials, Carlitz’s q-Bernoulli polynomials -polynomials, and the q-Bernoulli polynomials that emerge from the q-extension of the Hurwitz zeta function discussed here. 相似文献