On Certain Combinatorial Expansions of the Legendre-Stirling Numbers
Copyright policy )On Certain Combinatorial Expansions of the Legendre-Stirling Numbers
The Legendre-Stirling numbers of the second kind were introduced by Everitt et al. in the spectral theory of powers of the Legendre differential expressions. As a continuation of the work of Andrews and Littlejohn (Proc. Amer. Math. Soc., 137 (2009), 2581-2590), we provide a combinatorial code for Legendre-Stirling set partitions. As an application, we obtain expansions of the Legendre-Stirling numbers of both kinds in terms of binomial coefficients.
- Shanghai Jiao Tong University China (People's Republic of)
- Academia Sinica Taiwan
- Universidad del Noreste Mexico
Orthogonal polynomials, Arithmetic of Multiple Zeta Values and Related Functions, Stirling number, Combinatorial Mathematics and Algebraic Combinatorics, Set (abstract data type), Mathematical analysis, Orthogonal Polynomials, Gegenbauer polynomials, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Legendre transformation, Combinatorial proof, Generating function, Bell polynomials, Algebra and Number Theory, Associated Legendre polynomials, Stirling numbers of the first kind, Applied Mathematics, Physics, Classical orthogonal polynomials, Pure mathematics, Continuation, 05A05, 05A15, Computer science, Stirling numbers of the second kind, Programming language, Combinatorics, Physical Sciences, Legendre polynomials, Binomial coefficient, Thermodynamics, Combinatorics (math.CO), Legendre function, Mathematics, Stirling engine
Orthogonal polynomials, Arithmetic of Multiple Zeta Values and Related Functions, Stirling number, Combinatorial Mathematics and Algebraic Combinatorics, Set (abstract data type), Mathematical analysis, Orthogonal Polynomials, Gegenbauer polynomials, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Legendre transformation, Combinatorial proof, Generating function, Bell polynomials, Algebra and Number Theory, Associated Legendre polynomials, Stirling numbers of the first kind, Applied Mathematics, Physics, Classical orthogonal polynomials, Pure mathematics, Continuation, 05A05, 05A15, Computer science, Stirling numbers of the second kind, Programming language, Combinatorics, Physical Sciences, Legendre polynomials, Binomial coefficient, Thermodynamics, Combinatorics (math.CO), Legendre function, Mathematics, Stirling engine
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