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  Transformations
  
 
   
   Transformations and argument simplifications
   
  
    
    Argument involving basic arithmetic operations
    
   
     
     Involving csch-1(- z)
     
    Involving csch-1(-z) and csch-1(z) 
   
   
     
     Involving csch-1((z2)1/2)
     
    Involving sinh-1((z2)1/2) and csch-1(z) 
   
   
     
     Involving csch-1(a (b zc)m)
     
    Involving csch-1(a (b zc)m) and csch-1(a bm zm c) 
   
   
     
     Involving csch-1(1/(c z-1)1/2)
     
    Involving csch-1(1/(z-1)1/2) and csch-1(i/z1/2) 
    Involving csch-1(1/(z-1)1/2) and csch-1((-1/z)1/2) 
    Involving csch-1(1/(-z-1)1/2) and csch-1(1/z1/2) 
    Involving csch-1(1/(-z-1)1/2) and csch-1(1/z1/2) 
   
   
     
     Involving csch-1(1/c z-11/2)
     
    Involving csch-1(1/z-11/2) and csch-1(i/z1/2) 
    Involving csch-1(1/z-11/2) and csch-1((-1/z)1/2) 
    Involving csch-1(1/-z-11/2) and csch-1(1/z1/2) 
    Involving csch-1(1/-z-11/2) and csch-1(1/z1/2) 
   
   
     
     Involving csch -1(21/2/(c z-1)1/2)
     
    Involving csch-1(21/2/(-z-1)1/2) and csch-1(i/z) 
    Involving csch-1(21/2/(z-1)1/2) and csch-1(i/z) 
   
   
     
     Involving csch -1(2/c z-11/2)
     
    Involving csch-1(2/-z-11/2) and csch-1(i/z) 
    Involving csch-1(2/z-11/2) and csch-1(i/z) 
   
   
     
     Involving csch-1(z1/2/(-z-1)1/2)
     
    Involving csch-1(z1/2/(-z-1)1/2) and csch-1(z1/2) 
   
   
     
     Involving csch-1((-z)1/2/(z+1)1/2)
     
    Involving csch-1((-z)1/2/(z+1)1/2) and csch-1(z1/2) 
   
   
     
     Involving csch-1(z/-z-11/2)
     
    Involving csch-1(z/-z-11/2) and csch-1(z1/2) 
   
   
     
     Involving csch-1((2z)1/2/(a-z)1/2)
     
    Involving csch-1((2z)1/2/(-i-z)1/2) and csch-1(z) 
    Involving csch-1((2z)1/2/(i-z)1/2) and csch-1(z) 
    Involving csch-1((2z)1/2/(-z-1)1/2) and csch-1(i z) 
    Involving csch-1((2z)1/2/(1-z)1/2) and csch-1(i z) 
   
   
     
     Involving csch-1((-2z)1/2/(z-a)1/2)
     
    Involving csch-1((-2z)1/2/(i+z)1/2) and csch-1(z) 
    Involving csch-1((-2z)1/2/(z-i)1/2) and csch-1(z) 
    Involving csch-1((-2z)1/2/(z+1)1/2) and csch-1(i z) 
    Involving csch-1((-2z)1/2/(z-1)1/2) and csch-1(i z) 
   
   
     
     Involving csch-1(2z/a-z1/2)
     
    Involving csch-1((-2z/i+z)1/2) and csch-1(z) 
    Involving csch-1(2z/i-z1/2) and csch-1(z) 
    Involving csch-1(2z/-z-11/2) and csch-1(i z) 
    Involving csch-1(2z/1-z1/2) and csch-1(i z) 
   
   
     
     Involving csch-1(1/(-1-z2)1/2)
     
    Involving csch-1(1/(-1-z2)1/2) and csch-1(1/z) 
   
   
     
     Involving csch-1(1/-1-z21/2)
     
    Involving csch-1(1/-1-z21/2) and csch-1(1/z) 
   
   
     
     Involving csch-1(z/(-z2-1)1/2)
     
    Involving csch-1(z/(-1-z2)1/2) and csch-1(z) 
   
   
     
     Involving csch-1((z2)1/2/(-z2-1)1/2)
     
    Involving csch-1((z2)1/2/(-z2-1)1/2) and csch-1(z) 
   
   
     
     Involving csch-1((-z2)1/2/(z2+1)1/2)
     
    Involving csch-1((-z2)1/2/(z2+1)1/2) and csch-1(z) 
   
   
     
     Involving csch-1(z2/-z2-11/2)
     
    Involving csch-1(z2/-z2-11/2) and csch-1(z) 
   
   
     
     Involving csch-1(1/2 z (1+z2)1/2)
     
    Involving csch-1(1/2 z (1+z2)1/2) and csch-1(1/z) 
   
   
     
     Involving csch-1(z2/2 (z2-1)1/2)
     
    Involving csch-1(z2/2 (1+z2)1/2) and csch-1(z) 
   
   
     
     Involving csch-1(21/2/((1+z2)1/2-1)1/2)
     
    Involving csch-1(21/2/((1+z2)1/2-1)1/2) and csch-1(1/z) 
   
   
     
     Involving csch-1((2/((1+z2)1/2-1))1/2)
     
    Involving csch-1((2/((1+z2)1/2-1))1/2) and csch-1(1/z) 
   
   
     
     Involving csch-1((2z2)1/2/(z ((1+z2)1/2-1)1/2))
     
    Involving csch-1((2z2)1/2/(z ((1+z2)1/2-1)1/2)) and csch-1(1/z) 
   
   
     
     Involving csch-1(1/z (2z2/((1+z2)1/2-1))1/2)
     
    Involving csch-1(1/z (2z2/((1+z2)1/2-1))1/2) and csch-1(1/z) 
   
   
     
     Involving csch-1((2z)1/2/((z2+1)1/2-z)1/2)
     
    Involving csch-1((2z)1/2/((z2+1)1/2-z)1/2) and csch-1(z) 
   
   
     
     Involving csch-1((2z/((z2+1)1/2-z))1/2)
     
    Involving csch-1((2z/((z2+1)1/2-z))1/2) and csch-1(z) 
   
  
 
 
   
   Products, sums, and powers of the direct function
   
  Sums of the direct function 
  Differences of the direct function 
  Linear combinations of the direct function 
 
 
   
   Related transformations
   
  
    
    Sums involving the direct function
    
   Involving log(z) 
   Involving sin-1(z) 
   Involving cos-1(z) 
   Involving tan-1(z) 
   Involving cot-1(z) 
   Involving csc-1(z) 
   Involving sec-1(z) 
   Involving sinh-1(z) 
   Involving cosh-1(z) 
   Involving tanh-1(z) 
   Involving coth-1(z) 
   Involving sech-1(z) 
  
  
    
    Differences involving the direct function
    
   Involving log(z) 
   Involving sin-1(z) 
   Involving cos-1(z) 
   Involving tan-1(z) 
   Involving cot-1(z) 
   Involving csc-1(z) 
   Involving sec-1(z) 
   Involving sinh-1(z) 
   Involving cosh-1(z) 
   Involving tanh-1(z) 
   Involving coth-1(z) 
   Involving sech-1(z) 
  
  
    
    Linear combinations involving the direct function
    
   Involving log(z) 
   Involving sin-1(z) 
   Involving cos-1(z) 
   Involving tan-1(z) 
   Involving cot-1(z) 
   Involving sec-1(z) 
   Involving sinh-1(z) 
   Involving cosh-1(z) 
   Involving tanh-1(z) 
   Involving coth-1(z) 
   Involving sech-1(z) 
  
 
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