Absolutely and completely monotonic functions and sequences: Difference between revisions
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→Some important properties: It is called the Hausdorff moment problem. |
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* A sequence <math> \{\mu_n\}_0^\infty</math> is completely monotonic if and only if there exists an increasing function <math>\alpha(t)</math> on <math>[0,1]</math> such that
::<math> \mu_n = \int_0^1 t^n \, d\alpha(t), \quad n=0,1,2,\ldots</math>
:The determination of this function from the sequence is referred to as the [[Hausdorff moment problem]].
==Further reading==
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