(a) Show that the change of variables 5 = e-1 maps the Laguerre inner product (5.53) to the standard L2 inner product on [0, 1]. However, explain why this does not allow you to change Legendre polynomials into Laguerre polynomials.
(b) Describe the functions resulting from applying the change of variables to the modified Legendre polynomials (5.61) and their orthogonality properties.
(c) Describe the functions results from applying the inverse change of variables to the Laguerre polynomials (5.55) and their orthogonality properties.