Second Order Differential Equations

Gerhard Kristensson received his B.S. degree in mathematics and physics in 1973, and the Ph.D. degree in theoretical physics in 1979, both from the University of Göteborg, Sweden. In 1983 he was appointed Docent in theoretical physics at the University of Göteborg. During 1977-1984 he held a research position sponsored by the National Swedish Board for Technical Development (STU) and he was Lecturer at the Institute of Theoretical Physics, Göteborg from 1980-1984. In 1984-1986 he was a Visiting Scientist at the Applied Mathematical Sciences group, Ames Laboratory, Iowa State University. He held a Docent position at the Department of Electromagnetic Theory, Royal Institute of Technology, Stockholm during 1986-1989, and in 1989 he was appointed the Chair of Electromagnetic Theory at Lund Institute of Technology, Sweden. In 1992, 1997 and 2007 he was a Visiting Erskine Fellow at the Department of Mathematics, University of Canterbury, Christchurch, New Zealand. Currently, Gerhard Kristensson is a member of the Advisory Board of Inverse Problems, the Board of Editors of Wave Motion, and the Editorial and Review Board of Journal of Electromagnetic Waves and Applications and Progress in Electromagnetic Research. He is a Fellow of the Institute of Physics, and since 2006 he is the chairman of the Swedish National committee of Radio Science (SNRV) and official representative for Sweden in the International Union of Radio Science (URSI). From 1994-2005, he was the chairman of Commission B of SNRV and Official Member of URSI, Commission B for Sweden. Kristensson's major research interests are focused on wave propagation in inhomogeneous media, especially inverse scattering problems. During recent years the propagation of transient electromagnetic waves in complex media, such as dispersive anisotropic and bi-isotropic media, has been stressed. High frequency scattering methods, asymptotic expansions, optical fibers, antenna problems, and mixture formulas are also of interest, as well as radome design problems and homogenization of complex materials.

Preface.- Introduction.- Basic Properties of the Solutions.- Equations of the Fuchsian Type.- Equations with One to Four Regular Singular Points.- The Hypergeometric Differential Equation.- Legendre Functions and Related Functions.- Confluent Hypergeometric Functions.- Heun's Differential Equation.- The Gamma Function and Related Functions.- Difference Equations.- Partial Fractions.- Circles and Ellipses in the Complex Plane.- Elementary and Special Functions.- Notation.- Bibliography.- Index