Obtaining Generating Functions

Obtaining Generating Functions

by Elna B. McBride

Paperback(Softcover reprint of the original 1st ed. 1971)

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Product Details

ISBN-13: 9783642876844
Publisher: Springer Berlin Heidelberg
Publication date: 03/30/2012
Series: Springer Tracts in Natural Philosophy , #21
Edition description: Softcover reprint of the original 1st ed. 1971
Pages: 104
Product dimensions: 6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

I. Series Manipulation Methods.- First Part: Underlying Ideas.- 1. Introduction.- 2. The factorial function and the generalized hypergeometric functions.- 3. Obtaining generating functions from expansions in powers of x.- Second Part: Rainville’s Methods.- 4. Using an auxiliary variable.- 5. A bilinear generating function.- 6. Bilateral generating functions.- 7. Summary of results.- II. The Weisner Method.- 1. Introduction.- 2. The differential equation.- 3. Linear differential operators.- 4. Group of operators.- 5. The extended form of the group generated by B and C.- 6. Generating functions.- 7. Summary.- III. Further Results by the Weisner Method.- 1. Introduction.- 2. The modified Laguerre polynomials.- 3. The simple Bessel polynomials.- 4. The Gegenbauer polynomials.- IV. The Truesdell Method.- 1. Introduction.- 2. The ascending equation.- 3. The Hermite polynomials {Ha+n(x)}.- 4. The descending equation.- 5. The Hermite polynomials {Ha-n(x)}.- 6. The Charlier polynomials.- V. Miscellaneous Methods.- 1. Introduction.- 2. Classes of generating functions.- 3. Natural pairs of generating functions.- 4. Generating functions in differentiated form or in integrated form.- 5. Generating functions related by the Laplace transform.- 6. The contour integral method.- 7. Recent developments.

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