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There are several closely related functions called Jacobi theta functions, and many different and incompatible systems of notation for them. One Jacobi theta function (named after Carl Gustav Jacob Jacobi) is a function defined for two complex variables z and τ, where z can be any complex number and τ is the half-period ratio, confined to the upper half-plane, which means it has a positive ...
In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan theta. The function is named after mathematician Srinivasa ...
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help. Pages in category "Theta functions" The following 16 ...
theta functions; the angle of a scattered photon during a Compton scattering interaction; the angular displacement of a particle rotating about an axis; the Watterson estimator in population genetics; the thermal resistance between two bodies; ϑ ("script theta"), the cursive form of theta, often used in handwriting, represents
Download as PDF; Printable version ... There are a number of notational systems for the Jacobi theta functions. The notations given in the Wikipedia article define ...
If n = 1 and a and b are both 0 or 1/2, then the functions θ a,b (τ,z) are the four Jacobi theta functions, and the functions θ a,b (τ,0) are the classical Jacobi theta constants. The theta constant θ 1/2,1/2 (τ,0) is identically zero, but the other three can be nonzero.
The Neville theta functions are related to the Jacobi elliptic functions. If pq(u,m) is a Jacobi elliptic function (p and q are one of s,c,n,d), then If pq(u,m) is a Jacobi elliptic function (p and q are one of s,c,n,d), then
Typical singular behaviour of a theta function. It is the case, as the false-colour diagram indicates, that for a theta function the 'most important' point on the boundary circle is at z = 1; followed by z = −1, and then the two complex cube roots of unity at 7 o'clock and 11 o'clock.