# Theta function

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 (Math.) one of a group of functions used in developing the properties of elliptic functions.

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where [THETA](t) is the Heaviside Theta function. As the operators O(t, x) are uniformly inserted in the CFT, the dual bulk fields get sourced everywhere at the boundary of the Ad[S.sub.3].
The theta function of a characteristic m of degree g is the series
Define the theta function with real characteristics [5-7]
Ramanujan's general theta function f(a, b) is defined by
Employing the Jacobi triple product identity, we can derive the infinite product expressions for theta function.
Since for m = 1, [[bar.[psi]].sub.[bar.0]](q, q) = [[bar.[psi]].sub.[bar.0]] (q) is a mock theta function, hence by mathematical induction are mock theta functions.
In four cases it is already known that the product of two distinct Jacobian theta functions having the same variable z and the same nome q is a multiple of a single Jacobian theta function, with the multiple independent of z.
We will now show that the Jacobi theta function plays a central role in q-calculus.
Lastly, by performing a half left-shift transformation on a theta series, we get this mock theta function.
Putting a = 0 in Equation (4), we obtain the reciprocity law for the theta function, viz,
and the multivariate form of the partial theta function (see also , , )

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