Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Hermite Polynomial identity

  1. Jun 8, 2010 #1
    Does anyone know how to prove the following identity:

    [tex]\Sigma_{k=0}^{n}\left(\stackrel{n}{k}\right) H_{k}(x)H_{n-k}(y)=2^{n/2}H_{n}(2^{-1/2}(x+y))[/tex]

    where [tex]H_{i}(z)[/tex]represents the Hermite polynomial?
     
  2. jcsd
  3. Jun 9, 2010 #2
    I would try induction on n.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook