Results of Multidimensional Theta Functions

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21.7.E1 P ( λ , μ ) = 0 𝑃 𝜆 𝜇 0 {\displaystyle{\displaystyle P(\lambda,\mu)=0}} P*(lambda , mu) = 0 P*(\[Lambda], \[Mu]) == 0 Skipped - no semantic math Skipped - no semantic math - -
21.7.E11 μ 2 = Q ( λ ) superscript 𝜇 2 𝑄 𝜆 {\displaystyle{\displaystyle\mu^{2}=Q(\lambda)}} (mu)^(2) = Q*(lambda) \[Mu]^(2) == Q*(\[Lambda]) Skipped - no semantic math Skipped - no semantic math - -
21.7.E13 𝜼 ( T ) = 𝜼 ( T c ) 𝜼 𝑇 𝜼 superscript 𝑇 𝑐 {\displaystyle{\displaystyle\boldsymbol{{\eta}}(T)=\boldsymbol{{\eta}}(T^{c})}} eta*(T) = eta*((T)^(c)) \[Eta]*(T) == \[Eta]*((T)^(c)) Skipped - no semantic math Skipped - no semantic math - -
21.9.E1 4 u t = 6 u u x + u x x x 4 subscript 𝑢 𝑡 6 𝑢 subscript 𝑢 𝑥 subscript 𝑢 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle 4u_{t}=6uu_{x}+u_{xxx}}} 4*u[t] = 6*u*u[x]+ u[x*x*x] 4*Subscript[u, t] == 6*u*Subscript[u, x]+ Subscript[u, x*x*x] Skipped - no semantic math Skipped - no semantic math - -
21.9.E2 i u t = - 1 2 u x x + | u | 2 u 𝑖 subscript 𝑢 𝑡 1 2 subscript 𝑢 𝑥 𝑥 superscript 𝑢 2 𝑢 {\displaystyle{\displaystyle iu_{t}=-\tfrac{1}{2}u_{xx}+|u|^{2}u}} I*u[t] = -(1)/(2)*u[x*x]+(abs(u))^(2)* u I*Subscript[u, t] == -Divide[1,2]*Subscript[u, x*x]+(Abs[u])^(2)* u Skipped - no semantic math Skipped - no semantic math - -
21.9.E3 ( - 4 u t + 6 u u x + u x x x ) x + 3 u y y = 0 subscript 4 subscript 𝑢 𝑡 6 𝑢 subscript 𝑢 𝑥 subscript 𝑢 𝑥 𝑥 𝑥 𝑥 3 subscript 𝑢 𝑦 𝑦 0 {\displaystyle{\displaystyle(-4u_{t}+6uu_{x}+u_{xxx})_{x}+3u_{yy}=0}} - 4*u[t]+ 6*u*u[x]+ u[x*x*x][x]+ 3*u[y*y] = 0 Subscript[- 4*Subscript[u, t]+ 6*u*Subscript[u, x]+ Subscript[u, x*x*x], x]+ 3*Subscript[u, y*y] == 0 Skipped - no semantic math Skipped - no semantic math - -