Jacobi–Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression

W. N. Everitt, K.H. Kwon, Lance L. Littlejohn, R. Wellman, Gang-Joon Yoon

Type: Article

Publication Date: 2006-12-09

Citations: 80

DOI: https://doi.org/10.1016/j.cam.2006.10.045

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Locations

Journal of Computational and Applied Mathematics - View

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+	On Jacobi polynomials $${\mathscr {P}}_{k}^{(\alpha ,\beta )}$$ and coefficients $$c_{j}^{\ell }(\alpha ,\beta )$$ $$\left( k\ge 0, \ell =5,6; 1\le j\le \ell ; \alpha ,\beta > -1\right)$$	2020	Richard Olu Awonusika
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+	On the asymptotic normality of the Legendre–Stirling numbers of the second kind	2015	Wolfgang Gawronski Lance L. Littlejohn Thorsten Neuschel
+ PDF Chat	Properties and decompositions of domains for powers of the Jacobi differential operator	2020	Dale Frymark Constanze Liaw
+ PDF Chat	Combinatorial Interpretations of the Jacobi-Stirling Numbers	2010	Yoann Gelineau Jiang Zeng
+	Characterization of self-adjoint ordinary differential operators	2011	M. El-Gebeily Donal O’Regan Ravi P. Agarwal
+	Jacobi-Stirling polynomials and $P$-partitions	2012	Ira M. Gessel Zhicong Lin Jiang Zeng
+	The Jacobi-Stirling Numbers	2011	George E. Andrews Eric S. Egge Wolfgang Gawronski Lance L. Littlejohn
+ PDF Chat	Coefficientwise Hankel-total positivity of the row-generating polynomials for the output matrices of certain production matrices	2024	Bao-Xuan Zhu
+ PDF Chat	Perspectives on General Left-Definite Theory	2021	Dale Frymark Constanze Liaw

Works Cited by This (27)

Action	Title	Year	Authors
+	Linear differential operators	1967	M. A. Naĭmark
+	Advanced Combinatorics: The Art of Finite and Infinite Expansions	1974	Louis Comtet J.W. Nienhuys
+	Real and Complex Analysis.	1987	G. A. Garreau Walter Rudin
+ PDF Chat	None	2002	J. Arvesú Lance L. Littlejohn Francisco Marcellán
+	ON THE CONVERGENCE OF EIGENFUNCTION EXPANSIONS (II)	1957	E. C. Titchmarsh
+	The left-definite spectral theory for the classical Hermite differential equation	2000	W. N. Everitt Lance L. Littlejohn R. Wellman
+	A General Left-Definite Theory for Certain Self-Adjoint Operators with Applications to Differential Equations	2002	Lance L. Littlejohn R. Wellman
+	A Left-Definite Study of Legendre’s Differential Equation and of the Fourth-Order Legendre Type Differential Equation	2000	Rolf Vonhoff
+	PRODUCTS OF DIFFERENTIAL EXPRESSIONS WITHOUT SMOOTHNESS ASSUMPTIONS	1978	W. N. Everitt Anton Zettl
+	The Umbral Calculus	1984	Steven Roman