Page20,eq.1.3.29 e 2Ti(mix1+m2x2+m3x3)dx1dx2dx3 在元胞内积分,上下限为x1,x2,x3∈[,1],且m1,m2,m3∈Z 1,m=0 ellm 1 zm(22)m≠0 由于m∈Z,e2nm=1 2π lmid 0 0,m≠0 2ri(m1x1+m2x2+m3x3)dxldx2dx3= 1,m1=m2=m3=0 10,m1≠0或m2≠0或m3≠0Page20, eq. 1.3.29 �𝑒𝑒2𝜋𝜋𝑖𝑖(𝑚𝑚𝑚𝑚𝑚𝑚+𝑚𝑚𝑚𝑚𝑚𝑚+𝑚𝑚𝑚𝑚𝑚𝑚) 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 在元胞内积分，上下限为𝑥𝑥𝑥, 𝑥𝑥𝑥, 𝑥𝑥𝑥 ∈ [0, 1]，且𝑚𝑚𝑚, 𝑚𝑚𝑚, 𝑚𝑚𝑚 ∈ 𝑍𝑍 � 0 1 𝑒𝑒2𝜋𝜋𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑 = � 1, 𝑚𝑚 = 0 1 2𝜋𝜋𝑖𝑖𝑖𝑖 𝑒𝑒2𝜋𝜋𝑖𝑖𝑖𝑖 − 1 , 𝑚𝑚 ≠ 0 由于𝑚𝑚 ∈ 𝑍𝑍，𝑒𝑒2𝜋𝜋𝑖𝑖𝑖𝑖 = 1 � 0 1 𝑒𝑒2𝜋𝜋𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑 = � 1, 𝑚𝑚 = 0 0, 𝑚𝑚 ≠ 0 �𝑒𝑒2𝜋𝜋𝑖𝑖(𝑚𝑚𝑚𝑚𝑚𝑚+𝑚𝑚𝑚𝑚𝑚𝑚+𝑚𝑚𝑚𝑚𝑚𝑚) 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = � 1, 𝑚𝑚𝑚 = 𝑚𝑚𝑚 = 𝑚𝑚𝑚 = 0 0, 𝑚𝑚𝑚 ≠ 0 或 𝑚𝑚𝑚 ≠ 0 或 𝑚𝑚𝑚 ≠ 0