I want to test a difficult integral : Integral on all reals of some complicated function involving the Hermitian polynomials, exponentials, squares, factorials, and being general considering any Hermitian polynomials. I know the answer (it's ridiculously short compared with the statement) and just wanted to check. But why Mathematica doesn't calculate my integral ? (I'm quite new on the system and don't understand what causes the trouble) :
Integrate[(HermiteH[n, x/a]*Exp[-x^2/(2 a^2)]/((n!)^(1/2) (Pi a^2)^(1/4)))^2*x^2,
{x, -Infinity, Infinity},
Assumptions :> {Element[n, Integers], Element[a, Reals], a > 0}]
And getting as a result:
Integrate[ x^2 Exp[-(x^2/(2 a^2))]^2 HermiteH[n, x/a]^2/(Sqrt[a^2] Sqrt[Pi] n!), {x, -∞, ∞}, Assumptions :> {n ∈ Integers, a ∈ Reals, a > 0}]
What do I have to change to get an answer?
exp
toExp
, it is not possible to get analytical solution. !Mathematica graphics after about 3 minutes trying... also Maple 17 not able to do it. To help find such syntax errors, I always look at the equation for the green colored symbols (or is this blue colored? I always mix green with blue). If the symbol is not black colored, then it means Mathematica does not know about it. You could have seen thatexp
was green colored, this means Mathematica does know about it. $\endgroup$