On some connection results between Laguerre polynomials via third-order differential operator
Keyword(s):
Let $\{L^{(\alpha)}_n\}_{n\geq 0}$, ($\alpha\neq-m, \ m\geq1$), be the monic orthogonal sequence of Laguerre polynomials. We give a new differential operator, denoted here $\mathscr{L}^{+}_{\alpha}$, raises the degree and also the parameter of $L^{(\alpha)}_n(x)$. More precisely, $\mathscr{L}^{+}_{\alpha}L^{(\alpha)}_n(x)=L^{(\alpha+1)}_{n+1}(x), \ n\geq0$. As an illustration, we give some properties related to this operator and some other operators in the literature, then we give some connection results between Laguerre polynomials via this new operator.
2020 ◽
Vol 31
(4)
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pp. 585-606
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1975 ◽
Vol 72
(4)
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pp. 299-305
2015 ◽
Vol 13
(2)
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pp. 687-701
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2020 ◽
Vol 08
(12)
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pp. 2861-2868
Keyword(s):
Keyword(s):