Editing Moment problem (section)

{{Use American English|date = March 2019}}
{{Short description|Trying to map moments to a measure that generates them}}
[[File:Standard_deviation_diagram.svg|thumb|Example: Given the mean and variance <math>\sigma^2</math> (as well as all further  [[cumulant]]s equal 0) the [[normal distribution]] is the distribution solving the moment problem.]]
In [[mathematics]], a '''moment problem''' arises as the result of trying to invert the mapping that takes a [[measure (mathematics)|measure]] <math>\mu</math> to the sequence of [[Moment (mathematics)|moment]]s

:<math>m_n = \int_{-\infty}^\infty x^n \,d\mu(x)\,.</math>

More generally, one may consider
:<math>m_n = \int_{-\infty}^\infty M_n(x) \,d\mu(x)\,.</math>
for an arbitrary sequence of functions <math>M_n</math>.