Generalized harmonic number sums and quasisymmetric functions

Generalized Riie Shuues and Quasisymmetric Functions

Generalized Riffle Shuffles and Quasisymmetric Functions

Given a probability distribution on a totally ordered set, we define for each n ≥ 1 a related distribution on the symmetric group Sn, called the QS-distribution. It is a generalization of the q-shuffle distribution considered by Bayer, Diaconis, and Fulman. The QS-distribution is closely related to the theory of quasisymmetric functions and symmetric functions. We obtain explicit formulas in te...

Some results on q-harmonic number sums

In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit formulas for several classes of q-harmon...

Harmonic number sums in closed form

We extend some results of Euler related sums. Integral and closed form representation of sums with products of harmonic numbers and cubed binomial coefficients are developed in terms of Polygamma functions. The given representations are new. AMS subject classifications: Primary 11B65; Secondary 33C20

Partial Sums of Certain Harmonic Multivalent Functions

In this paper, we study the ratio of harmonic multivalent functions to its sequences of partial sums.