 Ursell function

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 s_{n} and cumulants (same as Ursell functions) u_{n} are related by the exponential formula:
(where E is the expectation).
The function was named after Harold Ursell, who introduced it in 1927.
References
 Glimm, James; Jaffe, Arthur (1987), Quantum physics (2nd ed.), Berlin, New York: SpringerVerlag, ISBN 9780387964768, MR887102
 Ursell, H. D. (1927), "The evaluation of Gibbs phaseintegral for imperfect gases", Proc. Cambridge Philos. Soc 23: 685–697, doi:10.1017/S0305004100011191
Categories: Statistical mechanics
 Theory of probability distributions
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