Chapter 19 Elliptic Integrals

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

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Acknowledgements:: 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:: Profile Bille C. Carlson, § ‣ Chapter Authors, § ‣ Associate Editors, Erratum (V1.0.1) for References, Erratum (V1.1.3) for Chapter 19, Version 1.2.0 (March 15, 2024), Notation for the Special Functions, Organization and Objective, § ‣ Software Cross Index
Permalink:: http://dlmf.nist.gov/19
Addition (effective with 1.0.1):: Armitage and Eberlein (2006) was added as a general reference for this chapter.