Origin of certain generating relations for modified Laguerre polynomials (Q2714483)

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scientific article; zbMATH DE number 1606939
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Origin of certain generating relations for modified Laguerre polynomials
scientific article; zbMATH DE number 1606939

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    20 June 2001
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    Origin of certain generating relations for modified Laguerre polynomials (English)
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    For the polynomial set \(M^{(\alpha)}_{\nu n}(x,q)\), \(\alpha= 0,1,2, \dots\) in the form NEWLINE\[NEWLINEM^{(\alpha)}_{\nu n}(x,q)= {1\over n!}x^{-\alpha-nq} e^{p_\nu(x)} T_q^n[x^\alpha e^{-p_\nu (n)}],NEWLINE\]NEWLINE \(T_q=x^{q+1}D\) of \(D\equiv {d\over dx}\), introduced by \textit{C. M. Joshi} and \textit{M. L. Prajapat} [Kyungpook Math. J. 15,191-199 (1975; Zbl 0316.33010)], the authors obtain a bilinear generating relation.
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