User:Egm6322.s12.team2.Xia/RP7.3

=R*8.4 -Legendre Function =

Given
the following pairs: $$\displaystyle \{P_{0},\, Q_{0}\},\,\{P_{1},\! Q_{1}\},\cdots\,,\{P_{4},\, Q_{4}\}$$ (8.4.1) Where

Find
1.Plot the 8.4.1 in separate figures. 2.Observe even-ness and odd-ness of 8.4.1 and guess the value of the scalar products:

$$\displaystyle =\int_{\mu=-1}^{\mu=+1}P_{i}(\mu)Q_{i}(\mu)du=?$$

Solution
$$\displaystyle $$