[理工] [工數] 成大100

[OKOK98 (UTN)]

 成大工數100第一題

 The first six Legendre polynomials are

 P0(x)=1

 P1(x)=x

 P2(x)=1/2 (3x^2-1)

 P3(x)=1/2 (5x^3-3x)

 P4(x)=1/8 (35x^4-30x^2+3)

 P5(x)=1/8 (63x^5-70x^3+15x)

 Find the first three positive values of λ for which the problem

 (1-x^2)y'' - 2xy' + λy = 0  y(0)=0,y(x),y'(x) bounded on[-1,1]

 has nontrivial solutions (solutions other than y(x)=0)

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推 endlesschaos:屬於有背有分的題目  λ=n(n+1)才有非零解  n為整數
→ endlesschaos:才會在 x = -1 及 x = 1 bounded  考試時再推來不及
→ ntust661:給予的邊界必須還要知道 λ = even 才有 y(0) = 0
→ ntust661:抱歉... λ = odd 才有XD
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