From "Complex Variables Demystified", 2008, page 102:
find the series representation for arcsinh(x).
(1) The Maclaurin theorem can be used to write a series representation of sinh(x). This is given by:
(2) The inverse will have some series expansion which we write as:
(3) We label the coefficents in the series expansion of sinh by:
We find that:
(4) Therefore it follows that:
My Question is as follows:
What are they doing in (3) to equate an and bn coefficients from sinh and arcsinh?