Conversion from Taylor expansion to continued fraction

Taylor expansion of cosine-related functions

             for

　　　　           for

　                   for

                for

Here, B is absolute values of Bernoulli numbers.

To convert these, we usually use the following formula

  (regular expression)

   in special form

as in 0216.

For arctan(x) and cot_1(x), we have other forms for outside ranges.

　　　　           for

　　　　    for

　　　　  for

and

                for

　　　　         for

　　　　      for

For example,

for

for

for

where each term at the last is in the special form of continued fraction.