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►All ellipticintegrals of the form (19.2.3) and many multiple integrals, including (19.23.6) and (19.23.6_5), are special cases of a multivariate hypergeometric function
…The -function is often used to make a unified statement of a property of several ellipticintegrals.
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►Spenceley and Spenceley (1947) tabulates , , , , for and to 12D, or 12 decimals of a radian in the case of .
►Curtis (1964b) tabulates , , for , , and (not ) to 20D.
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►Zhang and Jin (1996, p. 678) tabulates , , for and to 7D.
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►Ellipticintegrals appear in lattice models of critical phenomena (Guttmann and Prellberg (1993)); theories of layered materials (Parkinson (1969)); fluid dynamics (Kida (1981)); string theory (Arutyunov and Staudacher (2004)); astrophysics (Dexter and Agol (2009)).