Construct a Taylor series for:

(1/x) integral(e^(-t^2)dt) from 0 to x

and bound the error when truncating after n terms.

Question

Construct a Taylor series for:

(1/x) integral(e^(-t^2)dt) from 0 to x

and bound the error when truncating after n terms.

anonymous · Answer

to clarify: $$\int\limits_{0}^{x} e^{-t^2}dt$$
the integral is from 0 to x (it looks like infinity)

dumbcow · Answer

thanks for clarifying, thats what i thought it was and im not sure i can help with this one
is the taylor series to include the integral? because there is no anti-derivative , you can take derivative of whole thing and get e^(-x2)

dumbcow · Answer

course when you take derivatives you have to include the "1/x" as well so multiple uses of product rule ... ugly :{

anonymous · Answer

right :/ I've never even tried constructing a taylor series for an integral, so I'm pretty confused

dumbcow · Answer

@hartnn, could you take a look at this