COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

Necessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2013-10, Vol.88 (2), p.309-319
Hauptverfasser: QI, FENG, CERONE, PIETRO, DRAGOMIR, SEVER S.
Format: Artikel
Sprache:eng
Schlagworte:
Gamma function
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Zusammenfassung:Necessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972712001025