Titlebook: Quantum Calculus; Victor Kac,Pokman Cheung Textbook 2002 Victor Kac. 2002 Derivative.Hypergeometric function.Partition.Quantum Calculus.Qu

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-Binomial Coefficients and Linear Algebra over Finite Fields,In this chapter we explain an important combinatorial meaning of the .-binomial coefficients.

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-Trigonometric Functions,The .-analogues of the sine and cosine functions can be defined in anal-ogy with their well-known Euler expressions in terms of the exponential function.

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,More on Heine’s Formula and the General Binomial,Inspired by (13.16) and (13.17), it is natural to generalize the notion of a .-binomial in the following way.

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Ramanujan Product Formula,In this chapter, we apply Heine’s formula to prove a remarkable identity discovered by the Indian mathematician Ramanujan. This identity relates a . to an infinite product, and it has many interesting applications in number theory, which will be discussed in subsequent chapters.