Special Functions of Mathematical (Geo-)Physics

Willi Freeden: Studies in mathematics, geography, and philosophy at the RWTH Aachen, 1971 Diplom in mathematics, 1972 Staatsexamen in mathematics and geography, 1975 PhD in mathematics, 1979 Habilitation in mathematics, 1981/1982 visiting research professor at The Ohio State University, Columbus (Department of Geodetic Science and Surveying), 1984 professor of mathematics at the RWTH Aachen (Institute of Pure and Applied Mathematics), 1989 professor of technomathematics (industrial mathematics), 1994 head of the Geomathematics Group, 2002-2006 vice-president for Research and Technology at the University of Kaiserslautern, 2009 editor in chief of the International Journal on Geomathematics (GEM), 2010 editor of the Handbook of Geomathematics, member of the editorial board of seven international journals. Martin Gutting: Studies in mathematics at the University of Kaiserslautern, 2003 Diplom in mathematics, focus on geomathematics , 2007 PhD in mathematics, postdoc researcher at the University of Kaiserslautern, lecturer in the course of geomathematics (in particular for constructive approximation, special functions, and inverse problems), 2011 lecturer for engineering mathematics at the University of Kaiserslautern and DHBW Mannheim.

From the book reviews: "This is an erudite and competent book of great value, not only to specialists in the field. It should be very useful for both advanced students and active researchers in the field of geomathematics, geophysics, and geoengineering, and also for geooriented applied mathematicians. The style is superb and clear, and the organization is very well planned. I believe this excellent book should be required reading for all earth-oriented scientists." (Andrzej Icha, Pure and Applied Geophysics, Vol. 172, 2015) "This book provides an accessible and modern approach to special functions and applications to geomathematics, applied mathematics, environmental and engineering sciences. ... this will create new interest and useful leads for those engaged in the advanced study and research in special functions and their applications. ... book will continue to be very useful as a graduate level text and an interdisciplinary research reference for professionals in applied mathematics, geomathematics and harmonic analysis. ... this book is a new and excellent addition to the mathematics literature." (L. Debnath, Mathematical Reviews, October, 2013)

• 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.