1. you mean for arbitrary n,m.
2. what do you mean by z.
3. can you tell me how to evalute eq(15) to get this result: δ_n,m 2^n n! sqr(pi).
if I you will know how they get this result for Hn, Hm, so I can also evaluted for my equation with Hn * cos (...)
but this is my problem I dont know...
1. please, can tell me how to find the normalization coeffecient N_n?
2. you said different δ _n,m.
I know thet δ _n,m is Kronecker delta function, how it can be changed?
Thanks a lot!
Homework Statement
if H_n(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)
where n=1,2,...,N
from the orthogonality property of Hermite polynomials we will have:
\int^{\infty}_{-\infty} e^{-t^2} H_n(t) H_m(t)dt = \delta_n,m 2^n n! \sqrt{}pi
this gives
N_n=...
As I said to you:
let assume that our function g(t) instead of H(t)
So that,
g(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t)
we can say that g(t) can satisfied equations 15 and 17 because of its orthogonality properties.
Is that true?
according to the text that I have and I couldnt attached it here, the coeffecient C_m,n(t) is the the cross correlation function between nth and mth order pulses at point t.
let assume that our function g(t) instead of H(t)
So that,
g(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t)
1. we can say that g(t) can satisfied equations 15 and 17 because of its orthogonality properties.
Is that true?
2. in equation 18, I didnt understand what...
for Hn(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t)
where fc will be chosen such as to still keeping the orthogonality of Hn(t) for different integer values for n.
so,
Psi_n(t)= N_n * Hn(t)
where N_n = \frac{1}{\sqrt{2^n*n!*\sqrt{pi}}}
according to the definition as...