§19.35 Other Applications

ⓘ

Permalink:: http://dlmf.nist.gov/19.35
See also:: Annotations for Ch.19

§19.35(i) Mathematical
§19.35(ii) Physical

§19.35(i) Mathematical

ⓘ

Keywords:: Legendre’s elliptic integrals, Selberg integrals, applications, computation to high precision via elliptic integrals, generalizations of elliptic integrals, generalized elliptic integrals, mathematical, modular theorems, pi, symmetric elliptic integrals
Permalink:: http://dlmf.nist.gov/19.35.i
See also:: Annotations for §19.35 and Ch.19

Generalizations of elliptic integrals appear in analysis of modular theorems of Ramanujan (Anderson et al. (2000)); analysis of Selberg integrals (Van Diejen and Spiridonov (2001)); use of Legendre’s relation (19.7.1) to compute $\pi$ to high precision (Borwein and Borwein (1987, p. 26)).

§19.35(ii) Physical

ⓘ

Keywords:: Legendre’s elliptic integrals, applications, critical phenomena, elliptic integrals, fluid dynamics, lattice models of critical phenomena, layered materials, physical, string theory, symmetric elliptic integrals
Permalink:: http://dlmf.nist.gov/19.35.ii
See also:: Annotations for §19.35 and Ch.19

Elliptic integrals 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)).

§19.35 Other Applications

Contents

§19.35(i) Mathematical

§19.35(ii) Physical