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Delta amplitude

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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
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article