Title

Computation of certain infinite series of the form Sigma f(n)n(k) for arbitrary real-valued k

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

Appl. Math. Comput.

Keywords

Computation of infinite series; Generating functions; Fractional; calculus; Generalized Bell polynomials; Applications of Taylor series; GENERATING POLYNOMIALS; FRACTIONAL DERIVATIVES; BELL POLYNOMIALS; STIRLING NUMBERS; LEIBNIZ RULE; ASYMPTOTICS; 2ND-KIND; Mathematics, Applied

Abstract

We provide a general method from which one may obtain more arbitrary closed form solutions for infinite series of the form Sigma f(n)n(k), for k is an element of R and sufficiently well-behaved f(n). We illustrate the methods for the special case of f(n) = a(n)/!, obtaining generalizations to the Bell numbers and polynomials. (C) 2009 Elsevier Inc. All rights reserved.

Journal Title

Applied Mathematics and Computation

Volume

215

Issue/Number

3

Publication Date

1-1-2009

Document Type

Article

Language

English

First Page

1209

Last Page

1216

WOS Identifier

WOS:000269403200036

ISSN

0096-3003

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