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Airy Functions And Applications To Physicsby Olivier Vallée; Manuel Soares
World Scientific 2004; US$ 65.00The use of special functions, and in particular Airy functions, is rather common in physics. The reason may be found in the need, and even in the necessity, to express a physical phenomenon in terms of an effective and comprehensive analytical form for the whole scientific community. However, for the past twenty years, many physical problems have been resolved by computers. This trend is now becoming the norm as the importance of computers continues to grow. As a last resort, the special functions employed in physics will have to be calculated numerically, even if the analytic formulation of physics is of primary importance. more...
Theory and Applications of Special Functionsby Mourad E.H. Ismail; Erik Koelink
Springer 2005; US$ 199.00This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. It also includes an article by Askey, Ismail, and Koelink on Rahman's mathematical contributions and how they influenced the recent upsurge in the subject. more...
Vistas Of Special Functionsby Shigeru Kanemitsu
World Scientific 2007; US$ 75.40This is a unique book for studying special functions through zeta-functions. Many important formulas of special functions scattered throughout the literature are located in their proper positions and readers get enlightened access to them in this book. The areas covered include: Bernoulli polynomials, the gamma function (the beta and the digamma function), the zeta-functions (the Hurwitz, the Lerch, and the Epstein zeta-function), Bessel functions, an introduction to Fourier analysis, finite Fourier series, Dirichlet L-functions, the rudiments of complex functions and summation formulas. The Fourier series for the (first) periodic Bernoulli polynomial is effectively used, familiarizing the reader with the relationship between special functions... more...
Handbook of Special Functionsby Yury A. Brychkov
Taylor & Francis 2008; US$ 99.95Because of the numerous applications involved in this field, the theory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. This book provides coverage of special functions, which are used to help solve many difficult problems in physics, engineering, and mathematics. more...
Special Functions for Applied Scientistsby A. M. Mathai; Hans J. Haubold
Springer 2008; US$ 109.00Chapter 1 introduces elementary classical special functions. Gamma, beta, psi, zeta functions, hypergeometric functions and the associated special functions, generalizations to Meijer's G and Fox's H-functions are examined here. Discussion is confined to basic properties and selected applications. Introduction to statistical distribution theory is provided. Some recent extensions of Dirichlet integrals and Dirichlet densities are discussed. A glimpse into multivariable special functions such as Appell's functions and Lauricella functions is part of Chapter 1. Special functions as solutions of differential equations are examined. Chapter 2 is devoted to fractional calculus. Fractional integrals and fractional derivatives are discussed.... more...
The Special Functions and Their Approximationsby Luke
Elsevier 1969; US$ 135.00The Special Functions and Their Approximations: v. 1 more...
Special Functions and Their Approximations: v. 2by Luke
Elsevier 1969; US$ 160.00Special Functions and Their Approximations: v. 2 more...
Dual Sets of Envelopes and Characteristic Regions of Quasi-Polynomialsby Sui Sun Cheng
World Scientific 2009; US$ 94.00Existence and nonexistence of roots of functions involving one or more parameters has been the subject of numerous investigations. For a wide class of functions called quasi-polynomials, the above problems can be transformed into the existence and nonexistence of tangents of the envelope curves associated with the functions under investigation. In this book, we present a formal theory of the Cheng-Lin envelope method, which is completely new, yet simple and precise. This method is both simple — since only basic Calculus concepts are needed for understanding — and precise, since necessary and sufficient conditions can be obtained for functions such as polynomials containing more than four parameters. Since the underlying principles... more...
Zeta Functions over Zeros of Zeta Functionsby Andre Voros
Springer 2010; US$ 49.95The famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions) are analyzed through several zeta functions built over those zeros. These 'second-generation' zeta functions have surprisingly many explicit, yet largely unnoticed properties, which are surveyed here in an accessible and synthetic manner, and then compiled in numerous tables. No previous book has addressed this neglected topic in analytic number theory. Concretely, this handbook will help anyone faced with symmetric sums over zeros like Riemann's. More generally, it aims at reviving the interest of number theorists and complex analysts toward those unfamiliar functions, on the 150th anniversary of Riemann's... more...
