Integrals

Date: Aug 2, 2010

FPSAC 2010

I'm currently happy attendant of FPSAC 2010 (formal power series & algebraic combinatorics) in San Francisco. My talk on random walks in the plane has been the very first regular one, which means that I can now fully enjoy all the other ones. read more »

Attachment: 
application/pdf icon
randomwalks-fpsac2010.pdf
in
Date: Aug 18, 2009

CARMA workshop in Newcastle, 2009

On August 18, 2009, the University of Newcastle hosted a CARMA workshop on Multidimensional Numerical Integration and Special Function Evaluation. Besides enjoying very interesting talks it's been my pleasure to present, together with James Wan, on progress of our joint work with Jon Borwein, Peter Donovan and Dirk Nuyens on expectations of random walks. read more »

Attachment: 
application/pdf icon
randomwalkintegrals.pdf
in
Date: May 13, 2009

A trick for playing a multivariate integral

For suitable functions f the integral

$$ \int_0^{\infty} \int_0^{\infty} \ldots \int_0^{\infty} \frac{dx_1 dx_2 \cdots dx_n}{(f(x_1) + f(x_2) + \ldots + f (x_n))^{k+1}} $$

is equal to

$$ \frac{1}{k!} \int_0^{\infty} t^k \left( \int_0^{\infty} e^{- t f(x)} dx \right)^n dt . $$

To see why this is true, start with the last integral and write the n-th power of the inner integral as a multiple integral over variables x1, …, xn. Then change order of integration and evaluate read more »

in
Syndicate content