Hermite polynomials (1 Viewer)

[§eraphim]

http://nrich.maths.org/discus/messages/8577/7618.html?1076341239

i read this on a forum. how did they come up with the factor 2^n to change it from a monic polynomial?

also, how is the fact that L^2 space related to this? L^2 spaces have a norm that depends on the chosen weighting function rite?

 

[Affinity]

Coz.. hermite didn't like his polynomials with leading coefficient 1. J/K the real reason is that the hermite polynomials is supposed to have norm/size one with respect to the space
Well this has something to do with polynomials(functions) being orthogonal to each other, so L2 is a natural space to be in. C2[-infinity,infinity] has the problem of not being complete.

The weighting function effectively changes the measure on the space from L2(R,B,m)(just learnt that a few lectures ago) to L2(R,B,m')