Jaggis
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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.
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.
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