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Legendre's differential equation is given (1-x²)y" - 2xy + a(a + 1)y = 0, y = y(x), a ER, (1). too Looking for a solution of the form, y = y(x) = Σax" show that the recursive relation n=0 which satisfy the coefficients a are, n(n+1)-b an+2 = (n+2)(n+1) ·an, b = a(a + 1), n = 0,1,...

Legendre's differential equation is given (1-x²)y" - 2xy + a(a + 1)y = 0, y = y(x), a ER, (1). too Looking for a solution of the form, y = y(x) = Σax" show that the recursive relation n=0 which satisfy the coefficients a are, n(n+1)-b an+2 = (n+2)(n+1) ·an, b = a(a + 1), n = 0,1,...

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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EXERCISE 1B Legendre's differential equation is given (1-x²)y" - 2xy + a(a + 1)y = 0, y = y(x), a ≤R, (1). too Looking for a solution of the form, y = y(x) = Σax" show that the recursive relation n=0 which satisfy the coefficients an are, n(n+1)-b ・An an+2 = (n+2)(n+1) b = a(a + 1), n = 0,1,...
Transcribed Image Text:EXERCISE 1B Legendre's differential equation is given (1-x²)y" - 2xy + a(a + 1)y = 0, y = y(x), a ≤R, (1). too Looking for a solution of the form, y = y(x) = Σax" show that the recursive relation n=0 which satisfy the coefficients an are, n(n+1)-b ・An an+2 = (n+2)(n+1) b = a(a + 1), n = 0,1,...
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