Physical Sciences and Mathematics Commons^™

Q-Series With Applications To Binomial Coefficients, Integer Partitions And Sums Of Squares, Amna Abdul Baset Saif Saif Al Suwaidi

Theses

In this report we shall introduce q-series and we shall discuss some of their applications to the integer partitions, the sums of squares, and the binomial coefficients. We will present the basic theory of q-series including the most famous theorems and rules governing these objects such as the q-binomial theorem and the Jacobi’s triple identity. We shall present the q-binomial coefficients which roughly speaking connect the binomial coefficients to q-series, we will give the most important results on q-binomial coefficients, and we shall provide some of our new results on the divisibility of binomial coefficients. Moreover, we shall give some …