Approximation of a Completely Monotone Function.
CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES
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A function f on 0, infinity is completely monotone if it possesses derivatives of all orders, and the successive derivatives alternate in sign. It is shown that for each x the value of fx lies between any two consecutive partial sums of the expansion of fx in Taylor series. The given result can be applied to various functions such as the hypergeometric and confluent hypergeometric functions, which are widely used in applied mathematics. Some statistical applications are also given.
- Statistics and Probability