Authors:
Z. Sebestyén Gödöllö University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllö Hungary

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З. Щебещтяен Gödöllö University of Agricultural Sciences Department of Mathematics Faculty of Agricultural Engineering Páter K. U. 1 2103 Gödöllö Hungary

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Abstract  

Let −1<α≤0 and let

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$L_n^{(\alpha )} (x) = \frac{1}{{n!}}x^{ - \alpha } e^x \frac{{d^n }}{{dx^n }}(x^{\alpha + n} e^{ - x} )$$ \end{document}
be the generalizednth Laguerre polynomial,n=1,2,… Letx1,x2,…,xn andx*1,x*2,…,x*n−1 denote the roots ofLn(α) (x) andLn(α)′ (x) respectively and putx*0=0. In this paper we prove the following theorem: Ify0,y1,…,yn−1 andy1 ,…,yn are two systems of arbitrary real numbers, then there exists a unique polynomialP(x) of degree 2n−1 satisfying the conditions
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\begin{gathered} P\left( {x_k^* } \right) = y_k (k = 0,...,n - 1) \hfill \\ P'\left( {x_k } \right) = y_k^\prime (k = 1,...,n). \hfill \\ \end{gathered}$$ \end{document}
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Analysis Mathematica
Language English
Size B5
Year of
Foundation
1975
Volumes
per Year
1
Issues
per Year
4
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)