Stern Polynomials as Numerators of Continued Fractions

• Autorzy: A. Schinzel
• Języki publikacji: EN

Abstrakty

EN

It is proved that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence Bₙ(1). As an application, the degree of Bₙ(t) is expressed in terms of the binary expansion of n.

Kategorie tematyczne

• 11B83: Special sequences and polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: 62
• Numer: 1
• Strony: 23-27

Daty

wydano

2014

Twórcy

autor

A. Schinzel

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba62-1-3