Conversion from Taylor expansion to continued fraction

 

Taylor expansion of inverse hyperbolic functions

 

                 for

        for

  for

       for

                             for

                        for

 

Some of the functions above have different forms outside the domain above. For arcsinh(x) for example,

 

                    for

         for

        for

 

 

To convert all in general, we usually use the following formula

 

  (regular expression)

   in special form