- #ALMOST IMPOSSIBLE INTEGRALS SUMS AND SERIES SERIES#
- #ALMOST IMPOSSIBLE INTEGRALS SUMS AND SERIES DOWNLOAD#
This seems to be a chronic problem with Springer. The binding is a bit fragile, and care should be taken to not have it bend to the point where pages start falling out. There are also numerous integrals of similar difficulty on math.stackexchange with worked solutions by the community. One good book is Irresistible Integrals by Boros and Moll.
#ALMOST IMPOSSIBLE INTEGRALS SUMS AND SERIES SERIES#
A good place to start is becoming proficient with manipulating the gamma function, and sums and series in general. Therefore, I highly recommend reading other resources first. So despite the author's claim that a "good knowledge of calculus" is sufficient, the techniques learned in Calculus II alone simply won't cut it here. They are defined in the book whenever they are used, but it is clearly assumed that the reader has had some previous exposure to them. Some examples: gamma/digamma/polygamma, beta, Riemann zeta, polylogarithm, Dirichlet eta/beta, and fractional part functions Euler-Mascheroni and Catalan constants harmonic numbers etc.
The problems are of the form 'show that 'this integral' 'expression'', so that the solutions are given to you at the start. Each part has three chapters: the first on the problems, the second on hints, and the third on worked solutions. Special functions and constants are frequently employed. The book is split into two parts: the first is on definite integrals, and the second is on sums and series. The solutions are well-explained, though of course, a serious attempt should be made at solving the integrals before reading the author's explanations. They are in roughly ascending order of difficulty, but can be done in any order. The problems are of the form "show that 'this integral' = 'expression'", so that the solutions are given to you at the start. The book is split into two parts: the first is on definite integrals, and the second is on sums and series. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results.
#ALMOST IMPOSSIBLE INTEGRALS SUMS AND SERIES DOWNLOAD#
Download Table Of Integrals Series And Products books, Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. Gradshteyn, Table Of Integrals Series And Products Book available in PDF, EPUB, Mobi Format. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Almost Impossible Integrals Sums And Seriesby I. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. The mathematician Leonard Euler developed some surprising mathematical formulas involving the number #\pi#.This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. What about #\zeta(n)# when #n# is negative? Or a fraction?.Recurrence relations involving the coefficients.The next values of #S_n, C_n, \zeta_n#.Recurrence relations for #S_n(x)# and #C_n(x)#.Alternative derivation that doesn’t use delta-functions.Evaluating the infinite sum using a famous summation trick.Detour: The Fourier representation of the Delta function (which isn’t actually a function).Some related functions defined via Fourier series.
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