Generalized Stirling Numbers and Sums of Powers of Arithmetic Progressions

Autor/in	Cereceda, José Luis
Titel	Generalized Stirling Numbers and Sums of Powers of Arithmetic Progressions
Quelle	In: International Journal of Mathematical Education in Science and Technology, 51 (2020) 6, S.954-966 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2019.1688407
Schlagwörter	Numbers; Arithmetic; Mathematical Formulas; Computation + Suchen Sie Ihr Suchwort? Zahlenraum; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematische Formel
Abstract	In this paper, we first focus on the sum of powers of the first n positive odd integers, T[subscript k](n)=1[superscript k]+3[superscript k]+5[superscript k]+...+(2n-1)[superscript k], and derive in an elementary way a polynomial formula for T[subscript k](n) in terms of a specific type of generalized Stirling numbers. Then we consider the sum of powers of an arbitrary arithmetic progression and obtain the corresponding polynomial formula in terms of the so-called r-Whitney numbers of the second kind. This latter formula produces, in particular, the well-known formula for the sum of powers of the first n natural numbers in terms of the usual Stirling numbers of the second kind. Furthermore, we provide several other alternative formulas for evaluating the sums of powers of arithmetic progressions. (As Provided).
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Update	2024/1/01