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

    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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