Proving Orthogonality of Legendre Polynomials P3 and P1

[stunner5000pt]

To show that two Legendre polynomials(Pn and Pm) are orthogonal wht is the test that i have to use?

is it this?
$$\int_{-1}^{1} P_{n}(x)P_{m}(x) dx = 0$$

in that case to prove that P3 and P1 are orthogonal i have to use the above formula??

 

[HallsofIvy]

What is the definition of "orthogonal" in this case?

 

[aligator123]

you can also use rodriguez formula for this

 

[silviacipi]

legendre polynom in three dimension

Hello,
does anyone know the rule to obtain a general $$P^n$$ Legendre Polynomial in three dimension?

thanks!

 

[silviacipi]

sorry, I wronged:the rule to obtain the general $$P_n$$ Legendre Polynomial