Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A user gave the following nice answer

My question is that although it is clear $\log M_X(t)=Ct^2$ is a form that satisfies the condition $M_X^n(t/\sqrt{n})=M_X(t)$, how do you show no other form does?

My attempt: $\log M_X(t)$ can be written as $\alpha(t)t^2$ for some function $\alpha(t)$. Then $n\log M_X(t/\sqrt{n}) = n \alpha(t/\sqrt{n})t^2/n$. Letting $y=\sqrt{n}$, $\alpha(t)=\alpha(t/y)=\alpha(t/y^2)=\ldots $ so by continuity $\alpha(t)=\alpha(0)$, proving that $\alpha(t)$ is constant.

Any other ways of showing this?

share|cite|improve this question
Hmm, perhaps you could expand $M_X$ as a power series, and compare the coefficients of $M_X^n(t/\sqrt{n})$ and $M_X(t)$? – user1551 Nov 27 '12 at 15:34

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.