# What is the difference between contour and line integrals?

Hey everyone so I have a quick question about this integral symbol: $$\oint$$ I know that its referred to as a closed line integral for real functions usually like this: $$\oint_{C}$$or a closed contour integral for complex functions usually like this: $$\oint_{γ}$$ However is there a general name for this symbol? I heard that CLOSED CONTOUR INTEGRAL or PATH INTEGRAL are the names that cover each occasion but I am not sure. Also if it helps in greek this is referred to as the following: Επικαμπύλιο Ολοκλήρωμα meaning the integral over a curve.How could this be translated over to English?

• Would Mathematics be a better home for this question? Jan 17, 2023 at 20:38
• See this. As far as I am aware it does not have a specific name other than a "Contour/Path integral". The subscript symbol is just the name of the contour we're assessing around, I wouldn't worry about using certain letters for different types of functions. Jan 17, 2023 at 21:49
• "Line/path/contour integral" on their own are mutually synonymous, but "contour" tends to be associated more with integrals in the complex plane (anecdotally, anyway). "Path integral" seems to have another special meaning in quantum mechanics. Jan 17, 2023 at 22:46

$$\oint_C$$
is restricted for closed line integrals of real-valued functions. The inverse z-transform, for instance, is frequently denoted with $$\oint_C$$. That is right that $$\oint_\gamma$$ is also used, sometimes. But it seems to be a question of author taste. Not big deal.