Enterprise Risk Management Formula Book
2. Series expansions (for real-valued
functions)
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2.1 Exponential function and natural
logarithm (log)
function


2.2 Binomial expansion

where
is the binomial coefficient.
If we substitute into the binomial expansion
,
and
we
have (converges for any
if
):

A corollary is that:

2.3 Taylor series expansion
For one variable: if series converges (where
is the
’th
derivative of
and
,
etc.):

For more than one variable: e.g. for two variables,
if series converges (where
etc.):


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