A class of polynomials defined by generalized Rodrigues’ formula

Srivástava, H. M.; Singhal, J. P.

doi:10.1007/bf02415043

Cited by 33 publications

(28 citation statements)

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“…The polynomials G α n x r p q defined by where the parameters α, r, p, and q are unrestricted, in general (with, of course, q = 0), were introduced by Srivastava and Singhal [8] …”

Section: Further Applications Of Theoremmentioning

confidence: 99%

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

Srivástava

2000

Journal of Mathematical Analysis and Applications

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DEDICATED TO PROFESSOR GEORGE LEITMANNThe 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.

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“…The polynomials G α n x r p q defined by where the parameters α, r, p, and q are unrestricted, in general (with, of course, q = 0), were introduced by Srivastava and Singhal [8] …”

Section: Further Applications Of Theoremmentioning

confidence: 99%

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

Srivástava

2000

Journal of Mathematical Analysis and Applications

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“…(3.6) (x, r, p, a) are polynomials in x r introduced by us [9] in an attempt to provide an elegant unification of the various recent extensions of the classical Hermite and Laguerre polynomials given, for instance, by Gould and Hopper [4] and others referred to in our earlier paper [9]. A comparison of (31) with (1) would yield the following result: COROLLARY 8 If…”

Section: = σ S N (X)σ N (Y)r >mentioning

confidence: 96%

A class of bilateral generating functions for certain classical polynomials

Singhal¹,

Srivástava²

1972

Pacific J. Math.

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“…In 1968, Singh [17] studied the generalized Truesdell polynomials defined as: Srivastava and Singh [19] introduced a general class of polynomials in 1971 as:…”

Section: Interface Buildingmentioning

confidence: 99%