Hermite and Legendre polynomials

[terp.asessed]

Hi, I am just curious, are Hermite and Legendre polynomials related to one another? From what I have learned so far, I understand that they are both set examples of orthogonal polynomials...so I am curious if Hermite and Legendre are related to one another, not simply as sets of orthogonal polynomials...if anyone could elaborate, thanks!

 

[bhobba]

Its not something I know off the top of my head, but here is some detail:
http://math.stackexchange.com/questions/380345/connection-between-hermite-legendre-polynomials

Thanks
Bill

 

[dextercioby]

Of course there's a connection between them, as they are particular cases of hypergeometric functions (the confluent one is a limiting case of the Gauß one).

 

[terp.asessed]

Is

Gauß

a Gaussian function? If not, I've never heard of "Gauß"...

 

[jtbell]

I've never heard of "Gauß"...

German "ß" is spelled "ss" in other languages.

http://en.wikipedia.org/wiki/ß

 

[dextercioby]

Its not something I know off the top of my head, but here is some detail:
http://math.stackexchange.com/questions/380345/connection-between-hermite-legendre-polynomials

Thanks
Bill

There's also the reversed equation:

$$ P_n (x) = \frac{2}{n! \sqrt{\pi}} \int_{0}^{\infty} t^n e^{-t^2} H_n (xt) {}dt $$