Re: Alternative to bivariate Taylor series

*To*: mathgroup at smc.vnet.net*Subject*: [mg44651] Re: Alternative to bivariate Taylor series*From*: "Steve Luttrell" <luttrell at _removemefirst_westmal.demon.co.uk>*Date*: Wed, 19 Nov 2003 04:59:16 -0500 (EST)*References*: <bpd2a7$ce5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

You can do this by numerical integration as follows (insert whatever means and standard deviations you need in the Gaussian PDFs): In[11]:= a = NIntegrate[Log[1 + Exp[x - y]]*Exp[-x^2]*Exp[-y^2], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] Out[11]= 2.53231 In[12]:= b = NIntegrate[Exp[-x^2]*Exp[-y^2], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] Out[12]= 3.14159 In[13]:= a/b Out[13]= 0.806059 -- Steve Luttrell West Malvern, UK "koshi man" <man_koshi at yahoo.com> wrote in message news:bpd2a7$ce5$1 at smc.vnet.net... > Is there any expansion to log(1+exp(x-y)) other than > Taylor series in the integer powers of x and y ? > > I'm trying to find expectation of above function given > x, y are random variables with gaussian distributions > of known mean and variances. > > What about other bivariate expansions in Mathematica? > > CK > > __________________________________ > Do you Yahoo!? > Protect your identity with Yahoo! Mail AddressGuard > http://antispam.yahoo.com/whatsnewfree >