This is the mathematical reference book for the first and the second year graduate students who want to learn more about the application of certain techniques, to do calculations which happen to have interesting results in mathematical analysis.It is well known that we often need to establish some new sequences to converge to some fundamental constants with increasingly higher rate.Mathematical constants play a key role in several branches of mathematics.In this theory, an important concern is the definition of new sequences convergent to the mathematical constants with quicker rate of...

In this book, the problems with respect to the construction of the Fractal Interpolation Function and its application in the affine fractal sets are studied.Today, under the interests of many scholars, the research on the fractal theory has been developed deeply and fractal has most applications in the field of nature and society.The graph of the fractal interpolation function becomes the attractor against any Iterated Function System so IFS is a powerful mean to generate and analyze the new fractal interpolation function.It is the most important problem in fractal interpolation theory to...

In this book we consider the problems of estimating convergence and sum of series. Especially series with parameters is the remarkable one. In this book, we extend our remarkable results and offer wonderful methods to consider the convergence and sum of series with parameters.The book contains 4 chapters. Chapter 1 describes basic knowledge concerned with series. Chapter 2 deals with problems of estimating convergence and sum of series with parameters. Chapter 3 describes some hints helpful for the solution of the problems of chapter 2. Chapter 4 gives specific solutions to the problems of...

This book offers interesting problems specializing in several topics of mathematical analysis: limits, series, and integrals. The problems in our book, are closely related with the mathematical constants such as pi, Napier constant e, Euler's constant Gamma, and the special function such as the Gamma function , the Zeta function zeta.Such problems are so attractive and interesting for students and scholars, who deal in mathematical and engineering. Detailed solutions of problems are all given.The level of the problems is appropriate for the undergraduate-level mathematical contests.This book...

What we will discuss in this book is their application in the summation of series together with interesting formulas related to harmonic numbers. Harmonic numbers have been attracted the gaze of a large mathematicians for it's peculiar form and widely used in scientific and technical calculations. The results of the limits of sequences, infinite series and infinite products containing the harmonic number are very related with important mathematical constants like pi, Napier and Euler constants and special functions like Gamma and Riemann zeta functions. We have solved many series problems...

This book is the mathematical reference book which is helpful and accessible for not only professional mathematicians but also readers who have a little knowledge of mathematics. Special functions and mathematical constants are pervasive in all fields of science and industry. The gamma function can be thought of as an extension of the factorial function, which is defined only for positive integers. The most remarkable point of the book is the method to construct continued fraction approximation and its applications. The book consists of 3 chapters. In Chapter 1, we give the introduction for...

The sinc function is well known in people and have many interesting properties. These mathematical properties are well known in electrical engineers & physicists and used in many domains like signal processing.Since C.Stormer introduced his paper about those in 1885, many properties on sinc has been studied, generalized and results of these studies are introduced in preferences.This book is written to organize and explain the things of these properties which are studied much than others. In chapter 1, we introduce the fundamental knowledge which you need in order to understand chapter 2 and...

In this book, we are focused on solving the integration problems, one of the most difficult fields of theory of mathematical analysis and solving problems. People who learn or teach mathematical analysis know that, however the integrability of the integrand is well known, static integral calculations are generally difficult because of the nonexistence or inability of the primary function to calculate. Therefore, finding more effective and practical computing formulas or techniques for calculating definite integrals is an important way to enrich the content of mathematical analysis and solve...

This is a good mathematical reference book favorably available for readers who are interested in differential and integral calculus as well as experts who are engaged in mathematical field. Furthermore, this book aims at giving a lot of help to those who are eager to find something new and make a good invention.Many results in this book can encourage mathematicians and engineers who study special functions like gamma functions to be more active in their research work.In-depth study of gamma function led to a discovery that this function is closely related with many notable mathematical...