Special Functions (encyclopedia Of Mathematics And Its Applications)
by Ranjan Roy /
2001 / English / DjVu
4.1 MB Download
Special functions, which include the trigonometric functions, have
been used for centuries. Their role in the solution of differential
equations was exploited by Newton and Leibniz, and the subject of
special functions has been in continuous development ever since. In
just the past thirty years several new special functions and
applications have been discovered. This treatise presents an
overview of the area of special functions, focusing primarily on
the hypergeometric functions and the associated hypergeometric
series. It includes both important historical results and recent
developments and shows how these arise from several areas of
mathematics and mathematical physics. Particular emphasis is placed
on formulas that can be used in computation. The book begins with a
thorough treatment of the gamma and beta functions that are
essential to understanding hypergeometric functions. Later chapters
discuss Bessel functions, orthogonal polynomials and
transformations, the Selberg integral and its applications,
spherical harmonics, q-series, partitions, and Bailey chains. This
clear, authoritative work will be a lasting reference for students
and researchers in number theory, algebra, combinatorics,
differential equations, applied mathematics, mathematical
computing, and mathematical physics.
Special functions, which include the trigonometric functions, have
been used for centuries. Their role in the solution of differential
equations was exploited by Newton and Leibniz, and the subject of
special functions has been in continuous development ever since. In
just the past thirty years several new special functions and
applications have been discovered. This treatise presents an
overview of the area of special functions, focusing primarily on
the hypergeometric functions and the associated hypergeometric
series. It includes both important historical results and recent
developments and shows how these arise from several areas of
mathematics and mathematical physics. Particular emphasis is placed
on formulas that can be used in computation. The book begins with a
thorough treatment of the gamma and beta functions that are
essential to understanding hypergeometric functions. Later chapters
discuss Bessel functions, orthogonal polynomials and
transformations, the Selberg integral and its applications,
spherical harmonics, q-series, partitions, and Bailey chains. This
clear, authoritative work will be a lasting reference for students
and researchers in number theory, algebra, combinatorics,
differential equations, applied mathematics, mathematical
computing, and mathematical physics.
