Titlebook: Special Functions of Mathematical (Geo-)Physics; Willi Freeden,Martin Gutting Book 2013 Springer Basel 2013 Cauchy–Navier and Navier-Stoke

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Willi Freeden,Martin GuttingPresents special functions as essential tools contributing to solutions for geoscientific problems.Attractive textbook for the education in geomathematics.Addresses mathematicians, physicists, geo-eng

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Special Functions of Mathematical (Geo-)Physics978-3-0348-0563-6Series ISSN 2296-5009 Series E-ISSN 2296-5017

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Scalar Spherical Harmonics in ,p orthonormal function systems for scalar functions on spheres in the three-dimensional Euclidean space, namely the scalar spherical harmonics, which are then generalized to vectorial functions in Chap. 5 as well as to systems for scalar functions on spheres in the more general, q-dimensional setting in Chap. 6.

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Spherical Harmonics in ,ore extensive notation and makes some formulas a bit unwieldy. However, many proofs and the whole line of thought of the three-dimensional case carry over to the general setting such that we can skip some details that are analogous.

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Bessel Functions in , angular part. The Funk–Hecke formula (see Theorem 6.5.5) serves as the appropriate tool for decomposition. The angular part leads back to spherical harmonics, while the radial part satisfies a characteristic differential equation. Its solutions are the Bessel functions.

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Book 2013ured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality.The specia

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The Gamma Functionexplained in this chapter (for a more detailed discussion the reader is referred to, e.g., Artin (1964), Lebedev (1973), Müller (1998), Nielsen (1906), and Whittaker and Watson (1948) and the references therein).

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