■こんなところにもチェビシェフ多項式が現れる(その174)

 計算があわないのでいったん保留し,まとめておきたい.

  ξ=2mπ/h

  ξ1+ξn=ξ2+ξn-1=・・・=2π

  mi+mn-i+1=h

x=cosξ/2とおくと

[3^n-1]→Un(x)=0→cosjπ/(n+1)

[3^n-2,4]→Tn(x)=0→cos(2j−1)π/2n

[3^n-3,1,1]→xTn-1(x)=0→cos(2j−1)π/2(n−1)

[3^n-4,2,1]→Un(x)−xUn-5(x)=0

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 2x=2cosξ/2=yとおくと,

[3^3]→y^4−3y^2+1=0→ξ=2π/5

[3^2,1,1]→y(y^4−4y^2+2)=0→ξ=2π/8

[3^2,2,1]→(y^2−1)(y^4−4y^2+1)=0→ξ=2π/12

[3^3,2,1]→y(y^6−6y^4+9y^2−3)=0→ξ=2π/18

[3^4,2,1]→y^8−7y^6+14y^4−8y^2+1=0→ξ=2π/30

[3^5,2,1]→y(y^4−4)(y^2−1)(y^4−3y^2+1)=0→ξ=2π/0

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