𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Some Families of Generating Functions Associated with the Stirling Numbers of the Second Kind

✍ Scribed by H.M. Srivastava

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
127 KB
Volume
251
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

The object of this paper is to present a systematic introduction to (and several interesting applications of) a general result on generating functions (associated with the Stirling numbers of the second kind) for a fairly wide variety of special functions and polynomials in one, two, and more variables. The main results given below are shown to apply not only to the classical orthogonal polynomials including, for example, the Jacobi polynomials (which contain, as their special cases, the Gegenbauer or ultraspherical polynomials, the Legendre or spherical polynomials, and the Chebyshev polynomials of the first and second kinds) and the Laguerre polynomials, and to their various extensions and generalizations studied in recent years, but indeed also to a class of generalized hypergeometric functions, the Lauricella polynomials in several variables, and the familiar Lagrange polynomials which arise in certain problems in statistics. Relevant connections of some of these families of generating functions with various known results are also indicated.

πŸ“œ SIMILAR VOLUMES

Counting Pattern-free Set Partitions I:
Counting Pattern-free Set Partitions I: A Generalization of Stirling Numbers of the Second Kind
✍ Martin Klazar πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 160 KB

A partition u of [k] = {1, 2, . . . , k} is contained in another partition v of [l] if [l] has a k-subset on which v induces u. We are interested in counting partitions v not containing a given partition u or a given set of partitions R. This concept is related to that of forbidden permutations. A s

Annihilating polynomials for quadratic f
Annihilating polynomials for quadratic forms and Stirling numbers of the second kind
✍ Stefan De Wannemacker πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 144 KB

## Abstract We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non‐vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae an

Some Families of Generating Functions fo
Some Families of Generating Functions for the Bessel Polynomials
✍ Sheldon Yang; H.M Srivastava πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 177 KB

The main object of this paper is to show how readily some general results on bilinear, bilateral, or mixed multilateral generating functions for the Bessel polyno-Ε½ . mials would provide unifications and generalizations of numerous generating functions which were proven recently by using group-theor