Moment problem

In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequences of moments

m_n = \int_{-\infty}^\infty x^n \,d\mu(x)\,.\,\!

More generally, one may consider

m_n = \int_{-\infty}^\infty M_n(x) \,d\mu(x)\,.\,\!

for an arbitrary sequence of functions M_n.

单词	Moment problem
释义	Moment problem 英语百科 Moment problem In mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequences of moments $m_n = \int_{-\infty}^\infty x^n \,d\mu(x)\,.\,\!$ More generally, one may consider $m_n = \int_{-\infty}^\infty M_n(x) \,d\mu(x)\,.\,\!$ for an arbitrary sequence of functions M_n.
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