*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 |

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

*a*,

*b*] into

*a*=

*t*

_{0}<

*t*

_{1}< ... <

*t*

_{n}=

*b*and considering the expression

If γ is a continuously differentiable curve, the path integral can be evaluated as an integral of a function of a real variable:

## Vector calculus

*fill in*

## Quantum mechanics

*fill in*