In statistical mechanics, an Ursell function or connected correlation function, is a cumulant of a random variable. It is also called a connected correlation function as it can often be obtained by summing over connected Feynman diagrams (the sum over all Feynman diagrams gives the correlation functions).
If X is a random variable, the moments sn and cumulants (same as Ursell functions) un are related by the exponential formula:
(where E is the expectation).
The function was named after Harold Ursell, who introduced it in 1927.