Delta amplitude
From Encyclopedia of Mathematics
One of the three fundamental Jacobi elliptic functions. It is denoted by
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The delta amplitude is expressed as follows in terms of the Weierstrass sigma-function, the Jacobi theta-functions or a series:
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where is the modulus of the delta amplitude,
, and
,
. If
one has, respectively,
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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