Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Chapter 10:
The Confluent Hypergeometric Functions
Abstract
10.1 Introduction Whereas Gauss was largely responsible for the systematic study of the hypergeometric function, E. E. Kummer (1810–1893) is the person most associated with developing properties of the related confluent hypergeometric function. Kummer published his work on this function in 1836, and since that time it has been commonly referred to as Kummer's function. Like the hypergeometric function, the confluent hypergeometric function is related to a large number of other functions. Kummer's function satisfies a second-order linear differential equation called the confluent hypergeometric equation. A second solution of this DE leads to the definition of the confluent hypergeometric function of the second kind, which is also related to many other functions. At the beginning of the twentieth century (1904), Whittaker introduced another pair of confluent hypergeometric functions that now bears his name. The Whittaker functions arise as solutions of the confluent hypergeometric equation after a transformation to Liouville's standard form of the DE.
Online access to SPIE eBooks is limited to subscribing institutions.
CHAPTER 10


SHARE
Back to Top