Summation formulas of q-hyperharmonic numbers

Some q-Dixon-like summation formulas

We give a q-analogue of some Dixon-like summation formulas obtained by Gould and Quaintance [Fibonacci Quart. 48 (2010), 56–61] and Chu [Integral Transforms Spec. Funct. 23 (2012), 251–261], respectively. For example, we prove that

New Proofs of Some q-Summation and q-Transformation Formulas

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.

Some summation formulas involving harmonic numbers and generalized harmonic numbers

0 Summation Formulas for the product of the q - Kummer Functions from E q ( 2 )

Using the representation of Eq(2) on the non-commutative space zz ∗−qz∗z = σ; q < 1, σ > 0 summation formulas for the product of two, three and four q-Kummer functions are derived.

Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain fin...