MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

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

Let $$ f^{\alpha}_+(x)=\frac{1}{\Gamma(\alpha+1)}\sum_{k\ge 0}(-1)^k{\alpha+1 \choose k}(x-k)^{\alpha}_+, $$ where $\alpha > -\frac 12$. I am wondering if one can get nice representation of $L^2$-norm of the function $f^{\alpha}(x)$, namely $$ \int_{-\infty}^{\infty}(f^{\alpha}_+(x))^2dx. $$

(Here $y^{\alpha}_+=\max(0, y)^{\alpha}$ is a one-sided power function).

Thank you.

share|cite|improve this question
    
I fixed the Latex. – Ulrich Pennig May 16 '12 at 17:19
    
Cross-posted to MSE: math.stackexchange.com/questions/145188/… – Yemon Choi Jun 8 '12 at 21:19

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.