- 332 名前：１３２人目の素数さん mailto:sage [2020/02/13(木) 10:53:38.12 ID:Tf6czv/B.net]
- 4e(i+1,j)+ e(i-1,j)+ e(i,j+1)+ e(i,j-1)
=
∫[〜] (1-cos((x+y)(i+1))cos((x-y)j))/(1-cosxcosy)dxdy
+∫[〜] (1-cos((x+y)(i-1))cos((x-y)j))/(1-cosxcosy)dxdy
+∫[〜] (1-cos((x+y)i)cos((x-y)(j+1)))/(1-cosxcosy)dxdy
+∫[〜] (1-cos((x+y)i)cos((x-y)(j-1)))/(1-cosxcosy)dxdy
-4 ∫[〜] (1-cos((x+y)i)cos((x-y)j))/(1-cosxcosy)dxdy
=
∫[〜] (2-2cos(x+y)cos((x+y)i)cos((x-y)j))/(〜)dxdy
+∫[〜] (2-2cos(x-y)cos((x+y)i)cos((x-y)j))/(〜)dxdy
-4 ∫[〜] (1-cos((x+y)i)cos((x-y)j))/(1-cosxcosy)dxdy
=
∫[〜] 4(1-cos(x)cos(y)cos((x+y)i)cos((x-y)j))/(〜)dxdy
-∫[〜] 4(1-cos((x+y)i)cos((x-y)j))/(1-cosxcosy)dxdy
=
∫[〜] 4cos((x+y)i)cos((x-y)j))dxdy
=
δ[i0]δ[j0]16π^2
になるハズ。
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