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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