
EVOLUTIONARY MATHEMATICS AND SCIENCE FOR CALCULUS OF THE POWERED SUM OF A SEQUENCE OF NUMBERS
 Author(s):
 Hungping 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/vr88p538
 Abstract:
 Tsao, Hungping (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, Hungping (editors). Volume 3, Number 7, July 2021; 42 pages. Lenox Institute Press, Auburndale, MA, 02466, USA. No. STEAMVOL3NUM7JUL2021; ISBN 9780989087032. ..........ABSTRACT: We first use the difference equation method to come up with polynomial expressions of powered sums of the natural sequence, then transfer productsums to powersums 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 multilayer nested sums. In the end we derive some interesting results from the main theorem. ..........KEYWORDS: Difference equation, Integration, Productsum, Poweredsum, Natural sequence, Pascal triangle, Commutative ring, Arithmetically progressive sequence, Binomial coefficient, Stirling number, Bernoulli coefficient, ulayer nested sum.
 Notes:
 Volume 3, Number 7, No. STEAMVOL3NUM7JUL2021
 Metadata:
 xml
 Published as:
 Book chapter Show details
 Publisher:
 Lenox Institute Press, Auburndale, MA, 02466, USA.
 Pub. Date:
 July 2021
 Book Title:
 \"Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)\"
 Author/Editor:
 Wang, Lawrence K. and Tsao, Hungping (editors).
 Chapter:
 7
 Page Range:
 1  42
 ISBN:
 9780989087032
 Status:
 Published
 Last Updated:
 2 years ago
 License:
 All Rights Reserved

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