# Path integral

*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.

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* =

*t*_{0} <

*t*_{1} < ... <

*t*_{n} =

*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

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## Quantum mechanics

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