Thread: The linear approximation of a function
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Old October 21st, 2007, 07:28 AM
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For the record the multidimensional Taylor series around the point \bold{x} = \bold{a} is
T( \bold{x} ) = \sum_{ | \alpha | \geq 0 } \frac{D^{ \alpha } f( \bold{a} ) }{ \alpha ! } ( \bold{x} - \bold{a} )^{ \alpha }
where the expression employs multi-index notation. (I don't know the formula for the error term, sorry! But you can probably generalize it from the 1D Taylor series.)

-Dan
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