Оригинальная тета-функция Якоби 
  
    
      
        
          θ
          
            1
          
        
      
    
    {\displaystyle \theta _{1}}
  
 с 
  
    
      
        u
        =
        i
        
          π
        
        z
      
    
    {\displaystyle u=i{\pi }z}
  
 и номом[en] 
  
    
      
        q
        =
        
          e
          
            i
            
              π
            
            τ
          
        
        =
        0
        ,
        1
        
          e
          
            0
            ,
            1
            i
            π
          
        
      
    
    {\displaystyle q=e^{i{\pi }\tau }=0,1e^{0,1i\pi }}
  
}}. Соглашения:
 
  
    
      
        
          
            
              
                
                  θ
                  
                    1
                  
                
                (
                u
                ;
                q
                )
              
              
                
                =
                2
                
                  q
                  
                    
                      1
                      4
                    
                  
                
                
                  ∑
                  
                    n
                    =
                    0
                  
                  
                    ∞
                  
                
                (
                −
                1
                
                  )
                  
                    n
                  
                
                
                  q
                  
                    n
                    (
                    n
                    +
                    1
                    )
                  
                
                sin
                ⁡
                (
                2
                n
                +
                1
                )
                u
              
            
            
              
              
                
                =
                
                  ∑
                  
                    n
                    =
                    −
                    ∞
                  
                  
                    n
                    =
                    ∞
                  
                
                (
                −
                1
                
                  )
                  
                    n
                    −
                    
                      
                        1
                        2
                      
                    
                  
                
                
                  q
                  
                    
                      
                        (
                        
                          n
                          +
                          
                            
                              1
                              2
                            
                          
                        
                        )
                      
                      
                        2
                      
                    
                  
                
                
                  e
                  
                    (
                    2
                    n
                    +
                    1
                    )
                    i
                    u
                  
                
              
            
          
        
      
    
    {\displaystyle {\begin{aligned}\theta _{1}(u;q)&=2q^{\frac {1}{4}}\sum _{n=0}^{\infty }(-1)^{n}q^{n(n+1)}\sin(2n+1)u\\&=\sum _{n=-\infty }^{n=\infty }(-1)^{n-{\frac {1}{2}}}q^{\left(n+{\frac {1}{2}}\right)^{2}}e^{(2n+1)iu}\end{aligned}}}
function EllipticTheta[1,z,0.1*Exp[i*pi*1/10] in the complex plane.