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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 ...
The equation relates values of the Riemann zeta function at the points s and 1 − s, in particular relating even positive integers with odd negative integers. Owing to the zeros of the sine function, the functional equation implies that ζ(s) has a simple zero at each even negative integer s = −2n, known as the trivial zeros of ζ(s).
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
Zuma's Revenge , has arrived for PC and Mac. Right now, the game is exclusively available at publisher PopCap's site for $19.99, where you can also download a free demo as well.
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.).
Fruit will quickly help fill the Zuma-meter to finish a level. Chain bonusses (every consecutive shot makes a set of 3 or more balls; hitting fruit will not break the chain) can be quite a bit ...
Zuma's Revenge from PopCap arrived on Tuesday, and the puzzle game has already stolen away the better portion of our week. As you attempt to conquer the Zuma-verse, we wanted to give you three ...