Chapter 19 Elliptic Integrals

Acknowledgments:: The parts of this chapter that deal with Legendre’s integrals are based in part on Abramowitz and Stegun (1964, Chapter 17) by L. M. Milne-Thomson. I am greatly indebted to R. C. Winther for indispensable technical support and to F. W. J. Olver for long-sustained encouragement of a new approach to elliptic integrals. I thank E. Neuman for improvements to §§19.9 and 19.24(i).
Notes:: The main references used for writing this chapter are Erdélyi et al. (1953b), Byerly (1888), Cazenave (1969), and Byrd and Friedman (1971) for Legendre’s integrals, and Carlson (1977b) for symmetric integrals. For additional bibliographic reading see Armitage and Eberlein (2006), Cayley (1895), Greenhill (1892), Legendre (1825–1832), Tricomi (1951), and Whittaker and Watson (1927).
Referenced by:: Bille C. Carlson, Version 1.0.1 (June 27, 2011), Organization and Objective, Notation for the Special Functions, § ‣ § Software Cross Index
Permalink:: http://dlmf.nist.gov/19

Mathematics Department and Ames Laboratory (U.S. Department of Energy), Iowa State University, Ames, Iowa.