Conversion from Taylor expansion to continued fraction

Taylor expansion of hyperbolic functions

  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,…

For sinh(x)and cosh(x) in particular,

Here, we can apply the following formula

  in special form

as in 0215. That is,

Now we consider the following formula

in 0114. That is,

In the same way,

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

  (regular expression)

   in special form