Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 22

Taylor's theorem allows us to expand a function as a series involving higher-order derivatives of a function. We take the Cauchy form (with exact remainder):

 

(1.10)

and:

We conclude with a discussion of the exponential function. It is the only function that is the same as its derivative. To see this, we use the formal definition (1.7) of a derivative (and noting that ):

We summarise some useful properties of the exponential function: