Absolutely and completely monotonic functions and sequences: Difference between revisions

Revision as of 12:50, 29 December 2023

Revision as of 23:29, 29 December 2023

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The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain

Jacobi series.<ref>{{cite journal |last1=R. Askey |title=Summability of Jacobi series |journal=Transactions of American Mathematical Society |date=1973 |volume=179 |pages=71 - 84}}</ref> Such functions occur in other areas of mathematics areas such as probability theory, numerical analysis, and elasticity.<ref>{{cite book |last1=William Feller |title=An Introduction to Probability Theory and Its Applications, Vol. 2 |date=1971 |publisher=Wiley |___location=New York |edition=3}}</ref>

==Definitions==