0x222E

0x222E refers to the Unicode code point U+222E, which renders as the contour integral symbol ∮. It resides in the Mathematical Operators block of the Unicode standard and is used primarily in mathematics to denote contour integrals, i.e., integrals taken over a closed path in the complex plane.

A contour integral ∮_C f(z) dz is defined for a complex function f along a closed curve C. The value of the integral depends on the chosen path and its orientation; the standard convention is a positive, counterclockwise orientation. Contour integrals are central to complex analysis, with key results such as Cauchy’s integral theorem and the residue theorem enabling the evaluation of many integrals by examining the poles of the integrand inside the path.

Representation and encoding: In Unicode, U+222E is the character Contour Integral. In HTML, it can be rendered with the numeric character reference ∮ or ∞. In LaTeX, the symbol is produced with \oint. The contour integral notation is widely used in mathematics and theoretical physics to express integrals over closed paths, often in conjunction with functions defined on or analytic within regions of the complex plane.