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The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

Nonlinear systems. --- Exponential functions. --- Functions, Exponential --- Hyperbolic functions --- Systems, Nonlinear --- Mathematics. --- Fourier analysis. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Partial Differential Equations. --- Fourier Analysis. --- Mathematical Physics. --- Applications of Mathematics. --- Exponents (Algebra) --- Logarithms --- Transcendental functions --- System theory --- Differential equations, partial. --- Math --- Science --- Analysis, Fourier --- Mathematical analysis --- Partial differential equations --- Engineering --- Engineering analysis --- Physical mathematics --- Physics --- Mathematics

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This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Mathematics. --- Functions of complex variables. --- Differential equations. --- Functions of real variables. --- Sequences (Mathematics). --- Special functions. --- Astronomy. --- Astrophysics. --- Cosmology. --- Special Functions. --- Sequences, Series, Summability. --- Real Functions. --- Functions of a Complex Variable. --- Ordinary Differential Equations. --- Astronomy, Astrophysics and Cosmology. --- Astronomy --- Deism --- Metaphysics --- Astronomical physics --- Cosmic physics --- Physics --- Physical sciences --- Space sciences --- Special functions --- Mathematical analysis --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Real variables --- Functions of complex variables --- 517.91 Differential equations --- Differential equations --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Functions, special. --- Differential Equations. --- Bessel functions. --- Cylindrical harmonics --- Transcendental functions --- Bessel polynomials --- Harmonic analysis --- Harmonic functions