The Legendre equation of order is(1 x2)y 2xy + ( + 1)y = 0.The solution of this equation
Chapter 5, Problem 11(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 22and 23 of Section 5.3. In Example 4 of Section 5.4, it was shown that x = 1 are regularsingular 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 ofvariable x 1 = t and determine a series solution in powers of t.
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