• EVOLUTIONARY MATHEMATICS AND SCIENCE FOR NUMBERS INTRICACY INVESTIGATION

    Author(s):
    Hung-ping Tsao
    Editor(s):
    Hung-ping Tsao, Lawrence K Wang (see profile)
    Date:
    2019
    Group(s):
    Digital Books
    Subject(s):
    Mathematical sociology, Mathematics, Science--Study and teaching, Technology--Study and teaching, Educational evaluation
    Item Type:
    Book chapter
    Tag(s):
    stem, Steam, Science and technology studies (STS)
    Permanent URL:
    http://dx.doi.org/10.17613/pph5-6h91
    Abstract:
    Tsao, Hung-ping (2019). Evolutionary mathematics and science for numbers intricacy investigation. In: "Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)", Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 2, February 2019; 160 pages. Lenox Institute Press, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM2-FEB2019; ISBN 978-0-9890870-3-2. ---------------ABSTRACT: All foreseeable approaches to derive polynomial expressions for the power-sum of the natural sequence are presented here. Throughout, binomial coefficients play as the key role of linking together the product-sums and the power-sums. The author takes the opportunity to sort out the intricate liaisons among Stirling numbers of both kinds, Euler numbers of two orders, ordered and Eulerian Bell polynomials. He further generalizes the related numbers based on the natural sequence to those that are arithmetically progressive sequence based so that various structures of triangular arrays can be built on top of different underlying bases.
    Notes:
    KEYWORDS: STEM. STEAM. Polynomial expression, Natural sequence, Power-sum, Binomial coefficient, Product-sum, Stirling number, Pascal triangle, Alhazen’s Problem, Bernoulli coefficient, Arithmetically progressive sequence, Linear operator, Commutative ring, Recursive formula, n-layer integration, Sorting, Permutation, Combination, Cycle, Subset, Eulerian number, Stirling polynomial, Worpitzky’s identity, q-Gaussian coefficient, Bell number, Ordered Bell polynomial, Eulerian Bell polynomial,
    Metadata:
    xml
    Published as:
    Book chapter     Show details
    Publisher:
    Lenox Institute Press, Newtonville, NY, 12128-0405, USA.
    Pub. Date:
    February 2019
    Book Title:
    Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)
    Author/Editor:
    Lawrence K. Wang and Hung-ping Tsao
    Page Range:
    1 - 160
    ISBN:
    978-0-9890870-3-2
    Status:
    Published
    Last Updated:
    3 years ago
    License:
    All Rights Reserved
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