Delta amplitude
From Encyclopedia of Mathematics
One of the three fundamental Jacobi elliptic functions. It is denoted by
The delta amplitude is expressed as follows in terms of the Weierstrass sigma-function, the Jacobi theta-functions or a series:
where is the modulus of the delta amplitude, , and , . If one has, respectively,
See also Weierstrass elliptic functions; Elliptic function.
References
[1] | A. Hurwitz, R. Courant, "Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen" , Springer (1964) pp. Chapt. 3, Abschnitt 2 |
Comments
References
[a1] | H. Bateman (ed.) A. Erdélyi (ed.) et al. (ed.) , Higher transcendental functions , 2. Bessel functions, parabolic cylinder functions, orthogonal polynomials , McGraw-Hill (1953) pp. Chapt. 13 |
How to Cite This Entry:
Delta amplitude. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delta_amplitude&oldid=46622
Delta amplitude. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delta_amplitude&oldid=46622
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article