Search results
Results from the WOW.Com Content Network
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, the Riemann–Siegel theta function is defined in terms of the gamma function as = ((+)) for real values of t.Here the argument is chosen in such a way that a continuous function is obtained and () = holds, i.e., in the same way that the principal branch of the log-gamma function is defined.
The problem addressed by the circle method is to force the issue of taking r = 1, by a good understanding of the nature of the singularities f exhibits on the unit circle. The fundamental insight is the role played by the Farey sequence of rational numbers, or equivalently by the roots of unity :
An important application of spherical coordinates provides for the separation of variables in two partial differential equations—the Laplace and the Helmholtz equations—that arise in many physical problems. The angular portions of the solutions to such equations take the form of spherical harmonics.
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 ...
Dick Vitale said he's cancer-free after his fourth bout with the disease in just over three years. The 85-year-old ESPN college basketball analyst announced Thursday on social media that he got ...
Furthermore, the theta function of an even unimodular lattice of rank n is actually a modular form of weight n/2. The theta function of an integral lattice is often written as a power series in q = e 2 i π τ {\displaystyle q=e^{2i\pi \tau }} so that the coefficient of q n gives the number of lattice vectors of norm 2 n .
Saturated fat is problematic because it can raise LDL (bad) cholesterol levels which, studies show, can contribute to cardiovascular disease and other heart problems. This risk may be minimized by ...