The Legendre equation of order is (1 x2) y__ 2xy_ + ( + 1) y = 0. The solution of this
Chapter 5, Problem 7(choose chapter or problem)
The Legendre equation of order is (1 x2) y__ 2xy_ + ( + 1) y = 0. The solution of this equation near the ordinary point x = 0 was discussed in 17 and 18 of Section 5.3. In Example 4 of Section 5.4, it was shown that x = 1 are regular singular points. a. Determine the indicial equation and its roots for the point x = 1. b. Find a series solution in powers of x 1 for x 1 > 0. Hint: Write 1 + x = 2 + ( x 1) and x = 1 + ( x 1). Alternatively, make the change of variable x 1 = t and determine a series solution in powers of t.
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