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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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