Specializations of Generalized Laguerre Polynomials
نویسندگان
چکیده
Three specializations of a set of orthogonal polynomials with “8 different q’s” are given. The polynomials are identified as q-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
منابع مشابه
9 J ul 1 99 3 SPECIALIZATIONS OF GENERALIZED LAGUERRE POLYNOMIALS
The second author dedicates this paper to the one and only Dick Askey, his mathematical father. Abstract. Three specializations of a set of orthogonal polynomials with " 8 different q's " are given. The polynomials are identified as q-analogues of Laguerre polynomi-als, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
متن کاملThe Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients
In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...
متن کاملSpecializations of One-parameter Families of Polynomials
Let K be a number field, and let λ(x, t) ∈ K[x, t] be irreducible over K(t). Using algebraic geometry and group theory, we study the set of α ∈ K for which the specialized polynomial λ(x, α) is K-reducible. We apply this to show that for any fixed n ≥ 10 and for any number field K, all but finitely many K-specializations of the degree n generalized Laguerre polynomial L (t) n (x) are K-irreduci...
متن کاملNumerical solution of Fredholm integral-differential equations on unbounded domain
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کاملOctabasic Laguerre Polynomials and Permutation Statistics
A set of orthogonal polynomials with 8 independent “q’s” is defined which generalizes the Laguerre polynomials. The moments of the measure for these polynomials are the generating functions for permutations according to eight different statistics. Specializing these statistics gives many other well-known sets of combinatorial objects and relevant statistics. The specializations are studied, wit...
متن کامل