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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...
On a Class of Incomplete Gamma Functions with Applicationsby M. Aslam Chaudhry
CRC Press 2001; US$ 109.95The closed-form solutions to a considerable number of problems in applied mathematics, astrophysics, nuclear physics and engineering can be expressed in terms of the incomplete Gamma functions. This monograph provides a comprehensive study of incomplete Gamma functions. more...
Automorphic Forms And Shimura Varieties Of Pgsp(2)by Yuval Z Flicker
World Scientific 2005; US$ 95.00The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called ?liftings.? This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic... 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...
Polaritons in Periodic and Quasiperiodic Structuresby Eudenilson L. Albuquerque; Michael G. Cottam
Elsevier 2005; US$ 165.00In recent years there have been exciting developments in techniques for producing multilayered structures of different materials, often with thicknesses as small as only a few atomic layers. These artificial structures, known as superlattices, can either be grown with the layers stacked in an alternating fashion (the periodic case) or according to some other well-defined mathematical rule (the quasiperiodic case). This book describes research on the excitations (or wave-like behavior) of these materials, with emphasis on how the material properties are coupled to photons (the quanta of the light or the electromagnetic radiation) to produce ?mixed? waves called polaritons. · Clear and comprehensive account of polaritons in multilayered structures... 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...









