Some Absolutely Monotonic and Completely Monotonic Functions

1974 ◽  
Vol 5 (1) ◽  
pp. 58-63 ◽  
Author(s):  
Richard Askey ◽  
Harry Pollard
Keyword(s):  
Monotonic Functions ◽  
Completely Monotonic ◽  
Completely Monotonic Functions ◽  
Absolutely Monotonic

A Property of completely monotonic functions

1987 ◽  
Vol 42 (2) ◽  
pp. 143-146 ◽  
Author(s):  
Colm O'Cinneide
Keyword(s):  
Monotonic Functions ◽  
Completely Monotonic ◽  
Negative Function ◽  
Completely Monotonic Functions

AbstractA non-negative function f(t), t > 0, is said to be completely monotonic if its derivatives satisfy (-1)n fn (t) ≥ 0 for all t and n = 1, 2, …, For such a function, either f(t + δ) / f(t) is strictly increasing in t for each δ > 0, or f(t) = ce-dt for some constants c and d, and for all t. An application of this result is given.

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