Please identify a series expansion

[Jaggis]

Hi,

Could someone please identify the following series expansion for me, if possible:

$$f(x) = 1/h\int_x^{x+h}f(t)dt + A_{1}Δf(x) + A_{2}hΔf'(x) +...+ A_{m-1}h^{m-2}Δf^{(m-2)}(x) +r$$

where $$A_{m}$$ are, as far as I know, plain constants and $$Δ = [x, x+h]$$.

I think this result was partially obtained through using the Taylor's formula. It is a result that is used as a basis when constructing the Euler-Maclaurin summation formula.

I'd like to know how exactly this result follows. Thank you in advance.

 

[UltrafastPED]

Try looking for "Derivation of Euler-Maclaurin summation formula" - if you are correct you will find the related expressions.