Discrete Calculus By Analogy

Discrete Calculus By Analogy

Indexed in: Scopus

Discrete Hilbert-type inequalities including Hilbert's inequality are important in mathematical analysis and its applications. In 1998, the author presented an extension of Hilbert's integral ...
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Preliminary Concepts

Pp. 1-19 (19)

F. A. Izadi


For the purpose of being self-contained, the book starts with some elementary topics. These include the definition of various standard sets, some basic combinatorial definitions and identities, introducing complex numbers and their arithmetic properties, in particular de Moivre formula and the nth roots of a complex number. The case of square root gives rise to an elegant formula for the root of the real number of the form a± √b. The next two sections are devoted to the definitions and properties of matrices and determinants, the solutions of the linear system of equations as well as the formulas for some special determinants, in particular the Vandermonde determinant. Finally, the closing remark of the chapter is the definition of a function which plays an important role in discrete calculus. Because of its relation to the arrangement formula it is called "the arrangement power function".


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