       Are you familiar with the sos package?  Consider the following:


library(sos)
op <- findFn('orthogonal polynomial') # 165 links in 35 pkgs
ops <- findFn('orthogonal polynomials')#158 links in 35 pkgs
op. <- op |ops    #  194 links in 43 pkgs
save(op., file='orthopoly.rda')
summary(op.)
install.packages('orthopolynom')

gq <- findFn('gauss quadrature')   # 160 links in 50 pkgs
gnq <- findFn("gaussian quadrature")#129 links in 42 pkgs
gq. <- gq|gnq     #  219 links in 67 pkgs
summary(gq.)


       The print method for "op." or "gq." opens a web browser with a 
table of all the help pages matching the search term sorted to list 
first the package with the most matches with links to all the help 
pages.  A vignette explains more including how to generate a spreadsheet 
with a summary by package.


       One more thing:  As far as I know, the most general distribution 
capabilities in R is the "distr" package and companions like "distrEx".  
Unfortunately, I was not able to find anything for orthogonal 
polynomials or quadrature built on those packages, though it should not 
be too difficult to develop.


       Hope this helps.
       Spencer


On 10/10/2013 5:47 PM, Marino David wrote:
> Thanks so much for your response. BTW, do you know any Gauss 
> quadrature R package can deal with the arbitary PDF?
>
> Thank you!
>
> David
>
>
> 2013/10/11 Spencer Graves <spencer.graves@structuremonitoring.com 
> <mailto:spencer.graves@structuremonitoring.com>>
>
>     p.s.  Orthogonal polynomials can be defined for any probability
>     distribution on the real line, discrete, continuous, or otherwise,
>     as described in the Wikipedia article on "orthogonal polynomials".
>
>
>     On 10/10/2013 5:02 PM, Marino David wrote:
>>     Hi all,
>>
>>     We know that Hermite polynomial is for
>>     Gaussian, Laguerre polynomial for Exponential
>>     distribution, Legendre polynomial for uniform
>>     distribution, Jacobi  polynomial for Beta distribution. Does anyone know
>>     which kind of polynomial deals with the log-normal,
>
>
>           * lognormal in X is normal for Z = log(X).  Therefore, you'd
>     use Hermite polynomials in Z.
>
>
>>     Student’s t, Inverse
>>     gamma and Fisher’s F distribution?
>
>
>           * If X follows an F(d1, d2) distribution, then Z =
>     d1*x/(x1*x+d2) follows a beta distribution.  Use Jacobi
>     polynomials on Z.
>
>
>           * If X follows a student's t(df), then X^2 follows an F(1,
>     df) distribution.  Again, use Jacobi on the appropriate transform.
>
>
>           * If X follows an inverse gamma, then 1/X follows a gamma
>     distribution.
>
>
>           Does this answer the question?
>
>
>           Spencer
>>     Thank you in advance!
>>
>>     David
>>
>>     	[[alternative HTML version deleted]]
>>
>>
>>
>>     ______________________________________________
>>     R-help@r-project.org  <mailto:R-help@r-project.org>  mailing list
>>     https://stat.ethz.ch/mailman/listinfo/r-help
>>     PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
>>     and provide commented, minimal, self-contained, reproducible code.
>


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