Displaying similar documents to “On series, integrals and continued fractions, III”

q-Stern Polynomials as Numerators of Continued Fractions

Toufik Mansour (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We present a q-analogue for the fact 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. Moreover, we give a combinatorial interpretation for our q-analogue.

Stern Polynomials as Numerators of Continued Fractions

A. Schinzel (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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.

Hurwitz continued fractions with confluent hypergeometric functions

Takao Komatsu (2007)

Czechoslovak Mathematical Journal

Similarity:

Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions 0 F 1 ( ; c ; z ) . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.