# Important Functions That Are Multivariable Integrals

There are lots of "important" functions of one variable that are defined in terms of integrals for which no closed form exists, like the Gamma Function and the normal distribution. Are there any such functions that arise in the multivariable setting? I know that there are some elliptic integrals that take more than one variable. But, to me, they don't seem quite like the Gamma Function or the normal distribution.