Special Functions of Mathematical (Geo-)Physics

• Main Authors: Freeden, Willi. (Author), Gutting, Martin. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhũser, 2013.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Physical geography.; Meteorology.; Harmonic analysis.; Differential equations, partial.; Functions, special.; Special Functions.; Mathematical Physics.; Geophysics/Geodesy.; Partial Differential Equations.; Abstract Harmonic Analysis.; Meteorology/Climatology.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0348-0563-6

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the cau...

Table of Contents:

• 1 Introduction: Geomathematical Motivation
• Part I: Auxiliary Functions
• 2 The Gamma Function
• 3 Orthogonal Polynomials
• Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3
• 5 Vectorial Spherical Harmonics in R^3
• 6 Spherical Harmonics in R^q
• 7 Classical Bessel Functions
• 8 Bessel Functions in R^q
• Part III: Periodically Oriented Functions
• 9 Lattice Functions in R
• 10 Lattice Functions in R^q
• 11 Concluding Remarks
• References
• Index.