I have two Legendre questions, can anyone help me with either of them?
Suppose
. Let p be a polynomial. Show that
for some polynomial q.
Taking p(x) = 1 this implies
for some polynomial q.
and the other one is...
Use integration by parts to show that
Mr F says: The integration is over the interval (-1, 1).
for all
. Deduce that
is an orthogonal basis of
.
Mr F says: On the interval (-1, 1). may be
or it may be
... Im not sure really which is why im stuck! Both are used in my handout
Mr F says: They are equivalent expressions. The former is the series solution to Legendre's Equation. The latter is Rodrigues' Formula.