Talk:Hausdorff moment problem

Definition of difference operator
In my impression, the definition
 * $$(\Delta a)_n := a_{n+1} - a_n$$

is more common for the difference operator, as it fits nicely with the definition of derivative. In this notation, the requirement for a total monotone function would be
 * $$(-1)^r (\Delta^r a)_k \geq 0$$

for all $$r$$ and $$k$$, which emphasizes the fact that the sequence is monotonely decreasing, the first difference sequence monotonely increasing and so on. This is the way it is done in chapter VII of Feller, An Introducution to Probability Theory and Its Applications, vol. II.

Also, the condition $$\mu_k \leq 1$$ is needed. For simplicity I would let the sequence start at $$\mu_0$$ and require $$\mu_0 = 1$$, the conditions on the other $$\mu_k$$ then follow.

Unless somebody objects, I'll edit the article accordingly. —Preceding unsigned comment added by 141.20.28.32 (talk) 08:41, 3 August 2010 (UTC)


 * It seems that the changes requested above have been made. 67.198.37.16 (talk) 02:56, 15 January 2024 (UTC)