• EVOLUTIONARY MATHEMATICS AND SCIENCE FOR CALCULUS OF THE POWERED SUM OF A SEQUENCE OF NUMBERS

    Author(s):
    Hung-ping Tsao
    Editor(s):
    Lawrence K Wang (see profile)
    Date:
    2021
    Group(s):
    Science, Technology, Engineering, Arts and Mathematics (STEAM)
    Subject(s):
    Mathematics
    Item Type:
    Book chapter
    Tag(s):
    integration, calculus, powered sum, sequence of numbers
    Permanent URL:
    http://dx.doi.org/10.17613/vr88-p538
    Abstract:
    Tsao, Hung-ping (2021). Evolutionary mathematics and science for Calculus of the Powered Sums of a Sequence of Numbers. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 3, Number 7, July 2021; 42 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAM-VOL3-NUM7-JUL2021; ISBN 978-0-9890870-3-2. ..........ABSTRACT: We first use the difference equation method to come up with polynomial expressions of powered sums of the natural sequence, then transfer product-sums to power-sums in question to achieve the same goal. We next use the integration method for the same purpose and generalize them to arithmetically progressive sequence. We further introduce the multi-layer nested sums. In the end we derive some interesting results from the main theorem. ..........KEYWORDS: Difference equation, Integration, Product-sum, Powered-sum, Natural sequence, Pascal triangle, Commutative ring, Arithmetically progressive sequence, Binomial coefficient, Stirling number, Bernoulli coefficient, u-layer nested sum.
    Notes:
    Volume 3, Number 7, No. STEAM-VOL3-NUM7-JUL2021
    Metadata:
    Published as:
    Book chapter    
    Status:
    Published
    Last Updated:
    2 years ago
    License:
    All Rights Reserved

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