- Ay 1 X 0 A Singular Sturm Liouville Problem Is Given In The Range 1 X 1 P X Y Where P X Is A Known Function 1 (30.03 KiB) Viewed 35 times
Ay √1-x² =0, A singular Sturm-Liouville problem is given in the range -1≤x≤1: (p(x)y')'+- where p(x) is a known function and with some proper boundary conditions. It is known that all the solutions of this problem are polynomials and that there is one such polynomial T(x) for every degree n = 0, 1, 2,.... In particular, the first three polynomials can be written as: T(x)=1, T₁(x)=x, T₂(x)=x² + k, where keR is a number. a. Find the value of k in the definition of 7(x) (without relying on part d below). (10 points) b. Normalize T., that is, find TaT, such that 7-1. (5 points) = c. Find 2 (without relying on part d below). (5 points) d. Given that p(x)=√1-x² find 2. (5 points)