Exploring the Sums of Powers of Consecutive q-Integers

Autor/inn/en	Kim, T.; Ryoo, C. S.; Jang, L. C.; Rim, S. H.
Titel	Exploring the Sums of Powers of Consecutive q-Integers
Quelle	In: International Journal of Mathematical Education in Science & Technology, 36 (2005) 8, S.947-956 (10 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Quantitative Daten; Numbers; Mathematics Education; Mathematical Concepts; Equations (Mathematics); Theories; Computation; Problem Solving + Suchen Sie Ihr Suchwort? Zahlenraum; Mathematische Bildung; Equations; Mathematics; Gleichungslehre; Theory; Theorie; Problemlösen
Abstract	The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number theory, especially in connection with Fermat's last theorem (Ribenboin, 1979). They also appear in the calculus of finite differences (Norlund, 1924), in combinatorics (Comtet, 1970), and in other fields. Bernoulli polynomials and Bernoulli numbers possess many interesting properties and arise in many areas of mathematics and physics. This paper shows how to derive the sum of the nth powers of positive q-integers up to k-1, and displays the shapes of q-Bernoulli polynomials. (Contains 8 figures and 3 tables.) (ERIC).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10