In mathematics, theta functions are special functions of several complex variables. They appear in various topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory.
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The following formula yields the correct decimal digits of π up to 42 quadrillion digits. Also, see the general form. This high-precision approximation is related to the properties of theta functions or the Gaussian integral.

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