Conversion from Taylor expansion to continued fraction

Taylor expansion of hyperbolic functions

  for

                for

           for

Here, first several Bernoulli numbers are given by B₀=(-1), B₁=1/6, B₂=1/30, B₃=1/42,

B₄=1/30, B₅=5/66, B₆=691/2730,… E is absolute values of Euler numbers.

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

  (regular expression)

   in special form

For example,

  in special form