Sinhc函数
數學上的 Sinhc 函數定義如下

  
    
      
        Sinhc
        ⁡
        (z)
        =
        
          
            
              sinh
              ⁡
              (z)
            
            z
          
        
      
    
    {\displaystyle \operatorname {Sinhc} (z)={\frac {\sinh (z)}{z}}}
  ，它是下列微分方程的一個解：

  
    
      
        w
        (z)
        z
        −
        2
        
        
          
            d
            
              d
              z
            
          
        
        w
        (z)
        −
        z
        
          
            
              d
              
                2
              
            
            
              d
              
                z
                
                  2
                
              
            
          
        
        w
        (z)
        =
        0
      
    
    {\displaystyle w (z) z-2\,{\frac {d}{dz}} w (z)-z {\frac {d^{2}}{dz^{2}}} w (z)=0}
  

複域虛部
  
    
      
        Im
        ⁡
        
          (
          
            
              
                sinh
                ⁡
                (
                x
                +
                i
                y
                )
              
              
                x
                +
                i
                y
              
            
          
          )
        
      
    
    {\displaystyle \operatorname {Im} \left ({\frac {\sinh (x+iy)}{x+iy}}\right)}
  複域實部
  
    
      
        Re
        ⁡
        
          (
          
            
              
                sinh
                ⁡
                
                  (
                  
                    x
                    +
                    i
                    y
                  
                  )
                
              
              
                x
                +
                i
                y
              
            
          
          )
        
      
    
    {\displaystyle \operatorname {Re} \left ({\frac {\sinh \left (x+iy\right)}{x+iy}}\right)}
  絕對值
  
    
      
        
          |
          
            
              
                sinh
                ⁡
                (
                x
                +
                i
                y
                )
              
              
                x
                +
                i
                y
              
            
          
          |
        
      
    
    {\displaystyle \left|{\frac {\sinh (x+iy)}{x+iy}}\right|}
  一階導數
  
    
      
        
          
            
              cosh
              ⁡
              (z)
            
            z
          
        
        −
        
          
            
              sinh
              ⁡
              (z)
            
            
              z
              
                2
              
            
          
        
      
    
    {\displaystyle {\frac {\cosh (z)}{z}}-{\frac {\sinh (z)}{z^{2}}}}
  導數實部
  
    
      
        −
        Re
        ⁡
        
          (
          
            −
            
              
                
                  1
                  −
                  (
                  sinh
                  ⁡
                  (
                  x
                  +
                  i
                  y
                  )
                  
                    )
                    
                      2
                    
                  
                
                
                  x
                  +
                  i
                  y
                
              
            
            +
            
              
                
                  sinh
                  ⁡
                  (
                  x
                  +
                  i
                  y
                  )
                
                
                  (
                  x
                  +
                  i
                  y
                  
                    )
                    
                      2
                    
                  
                
              
            
          
          )
        
      
    
    {\displaystyle -\operatorname {Re} \left (-{\frac {1-(\sinh (x+iy))^{2}}{x+iy}}+{\frac {\sinh (x+iy)}{(x+iy)^{2}}}\right)}
  導數虛部
  
    
      
        −
        Im
        ⁡
        
          (
          
            −
            
              
                
                  1
                  −
                  (
                  sinh
                  ⁡
                  (
                  x
                  +
                  i
                  y
                  )
                  
                    )
                    
                      2
                    
                  
                
                
                  x
                  +
                  i
                  y
                
              
            
            +
            
              
                
                  sinh
                  ⁡
                  (
                  x
                  +
                  i
                  y
                  )
                
                
                  (
                  x
                  +
                  i
                  y
                  
                    )
                    
                      2
                    
                  
                
              
            
          
          )
        
      
    
    {\displaystyle -\operatorname {Im} \left (-{\frac {1-(\sinh (x+iy))^{2}}{x+iy}}+{\frac {\sinh (x+iy)}{(x+iy)^{2}}}\right)}
  絕對值
  
    
      
        
          |
          
            −
            
              
                
                  1
                  −
                  (
                  sinh
                  ⁡
                  (
                  x
                  +
                  i
                  y
                  )
                  
                    )
                    
                      2
                    
                  
                
                
                  x
                  +
                  i
                  y
                
              
            
            +
            
              
                
                  sinh
                  ⁡
                  (
                  x
                  +
                  i
                  y
                  )
                
                
                  (
                  x
                  +
                  i
                  y
                  
                    )
                    
                      2
                    
                  
                
              
            
          
          |
        
      
    
    {\displaystyle \left|-{\frac {1-(\sinh (x+iy))^{2}}{x+iy}}+{\frac {\sinh (x+iy)}{(x+iy)^{2}}}\right|}