A lattice path model for the Bessel polynomials
نویسنده
چکیده
The (n 1)th Bessel polynomial is represented by an exponential generating function derived from the number of returns to 0 of a sequence with 2n increments of 1 which starts and ends at 0. AMS 1991 subject classi cation. Primary: 05A15. Secondary: 33C10, 33C45. It is well known [21, x3.71 (12)],[6, (7.2(40)] that the McDonald function or Bessel function of imaginary argument K (x) := 1 2 x 2 Z 1 0 t e t (x=2) =t dt (1) admits the evaluation Kn+1=2(x) = r 2x e x n(x)x n (n = 0; 1; 2; : : :) (2) Research supported in part by N.S.F. Grant 97-03961
منابع مشابه
Asymptotics of basic Bessel functions and q-Laguerre polynomials
We establish a large n complete asymptotic expansion for q-Laguerre polynomials and a complete asymptotic expansion for a q-Bessel function of large argument. These expansions are needed in our study of an exactly solvable random transfer matrix model for disordered electronic systems. We also give a new derivation of an asymptotic formula due to Littlewood (1907).
متن کاملThe skew Schubert polynomials
We obtain a tableau definition of the skew Schubert polynomials named by Lascoux, which are defined as flagged double skew Schur functions. These polynomials are in fact Schubert polynomials in two sets of variables indexed by 321-avoiding permutations. From the divided difference definition of the skew Schubert polynomials, we construct a lattice path interpretation based on the Chen-Li-Louck ...
متن کاملThe Generalized Bessel Matrix Polynomials
Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...
متن کاملLattice path matroids: enumerative aspects and Tutte polynomials
Fix two lattice paths P and Q from ð0; 0Þ to ðm; rÞ that use East and North steps with P never going above Q: We show that the lattice paths that go from ð0; 0Þ to ðm; rÞ and that remain in the region bounded by P and Q can be identified with the bases of a particular type of transversal matroid, which we call a lattice path matroid. We consider a variety of enumerative aspects of these matroid...
متن کاملSome Generating Functions for Bessel Function by Using Lie Theoretic Method
This paper is an attempt is made to obtain Generating functions of modified Bessel Function. We can find number of generating functions for various special function and orthogonal polynomials by the application of group-theoretic method introduced by Louis Weisner.The process may also lead to some new generating functions for corresponding special functions. Bessel Function and orthogonal polyn...
متن کامل