Physics · Mathematical Methods
A polynomial Cn(x) of degree n defined on the domain x ∈ [-1, 1] satisfies the differential equation (1 - x2) d2Cn/dx2 - x dCn/dx + n2 Cn = 0. The polynomials satisfy the orthogonality relation ∫-11 σ(x) Cn(x) Cm(x) dx = 0 for n ≠ m. What is the weighting function σ(x)?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1e-x2
- 21
- 3(1 - x2)
- 4(1 - x2)-1/2✓
Correct answer
(1 - x2)-1/2
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