Main Page | See live article | Alphabetical index This is not about "path integrals" in the sense that means that which was studied by Richard Feynman. See Functional integration. In mathematics, a path integral is an integral where the function to be integrated is evaluated along a path or curve. Various different path integrals are in use. Table of contents 1 Complex analysis 2 Vector calculus 3 Quantum mechanics Complex analysis The path integral is a fundamental tool in complex analysis, where it is also called a contour integral. Suppose U is an open subset of C, γ : [a, b] → U is a rectifiable curve and f : U → C is a function. Then the path integral may be defined by subdividing the interval [a, b] into a = t0 < t1 < ... < tn = b and considering the expression The integral is then the limit as the distances of the subdivision points approach zero. If γ is a continuously differentiable curve, the path integral can be evaluated as an integral of a function of a real variable: Important statements about path integrals are given by the Cauchy integral theorem and Cauchy's integral formula. Vector calculus fill in Quantum mechanics fill in This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.