Corpus ID: 11132576

Some classes of completely monotonic functions

@inproceedings{Alzer2002SomeCO,
  title={Some classes of completely monotonic functions},
  author={H. Alzer and C. Berg},
  year={2002}
}
  • H. Alzer, C. Berg
  • Published 2002
  • Mathematics
  • We prove: (i) Let F n (r) = P n (x)[e - (1 + 1/x) x ] and G n (x) = P n (x)[(1 + 1/x) x + 1 - e], where P n (x) = x n + Σ n - 1 v = 0 c v , x v is a polynomial of degree n > 1 with real coefficients. F n is completely monotonic if and only if n = 1 and c 0 ≥ 11/12; and G n is completely monotonic if and only if n = 1 and c 0 ≥ 1/12. (ii) The functions x → e - (1 + 1/x) x and x → (1 + 1/x) x + 1 - e are Stieltjes transforms and in particular they are completely monotonic. (iii) Let a > 0 and b… CONTINUE READING
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