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1
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Linearization of the product of orthogonal polynomials of a discrete variable

100%
Belmehdi S., Lewanowicz S., Ronveaux A.
Applicationes Mathematicae
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1996-1997
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tom 24
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nr 4
445-455
EN
Let {$P_k$} be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in $P_iP_j=\sum_kc(i,j,k)P_k$, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by {$P_k$}.
2
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A fast algorithm for the construction of recurrence relations for modified moments

100%
Lewanowicz S.
Applicationes Mathematicae
|
1993-1995
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tom 22
|
nr 3
359-372
EN
A new approach is presented for constructing recurrence relations for the modified moments of a function with respect to the Gegenbauer polynomials.
3
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On a new generalization of Jacobsthal quaternions and several identities involving these numbers

100%
Bród D., Szynal-Liana A.
Commentationes Mathematicae
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2019
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tom 59
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nr 1-2
EN
In this paper we generalize Jacobsthal quaternions to \((s,p)\)\dywiz Jacobsthal quaternions. We give some of their properties, among others the Binet formula, the generating function and the matrix representation of these quaternions. We will show how a~graph interpretation can be used in proving some identities for quaternions.
4
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On Pell and Pell−Lucas Hybrid Numbers

88%
Szynal-Liana A., Włoch I.
Commentationes Mathematicae
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2018
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tom 58
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nr 1-2
EN
In this paper we introduce the Pell and Pell−Lucas hybrid numbers as special kinds of hybrid numbers. We describe some properties of Pell hybrid numbers and Pell−Lucas hybrid numbers among other we give the Binet formula, the character and the generating function for these numbers.
5
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Linearization of Arbitrary products of classical orthogonal polynomials

88%
Hounkonnou M. N., Belmehdi S., Ronveaux A.
Applicationes Mathematicae
|
2000
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tom 27
|
nr 2
187-196
EN
A procedure is proposed in order to expand $w=\prod^N_{j=1} P_{i_j}(x)=\sum^M_{k=0} L_ k P_ k(x)$ where $P_i(x)$ belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) ($M=\sum^N_{j=1} i_j$). We first derive a linear differential equation of order $2^N$ satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients $L_k$. We develop in detail the two cases $[P_i(x)]^N$, $P_ i(x)P_ j(x)P_ k(x)$ and give the recurrencerelation in some cases (N=3,4), when the polynomials $P_i(x)$are monic Hermite orthogonal polynomials.
6
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Recurrence relations for conditional moment generating functions of order statistics and record values

88%
AL-Hussaini E., Ahmad A. E.-B., El-Boghdady H.
Discussiones Mathematicae Probability and Statistics
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2005
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tom 25
|
nr 2
181-205
EN
In this paper, recurrence relations for conditional moment generating functions and conditional moments of order statistics and record values based on random samples drawn from members of a class of doubly truncated distributions Ád are obtained.
7
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k-th rekord values from Dagum distribution and characterization

63%
Kumar D.
Discussiones Mathematicae Probability and Statistics
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2016
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tom 36
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nr 1-2
25-41
EN
In this study, we gave some new explicit expressions and recurrence relations satisfied by single and product moments of k-th lower record values from Dagum distribution. Next we show that the result for the record values from the Dagum distribution can be derived from our result as special case. Further, using a recurrence relation for single moments and conditional expectation of record values we obtain characterization of Dagum distribution. In addition, we use the established explicit expression of single moment to compute the mean, variance, coefficient of skewness and coefficient of kurtosis. Finally, we suggest two applications.
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