Lubbock's Formula

f_0+f_(1/m)+f_(2/m)+...+f_r
=m(f_0+f_1+...+f_r)-1/2(m-2)(f_r+f_0)-(m^2-1)/(12m)(Deltaf_(r-1)-Deltaf_0)-(m^2-1)/(24m)(Delta^2f_(r-2)+Delta^2f_0)-((m^2-1)(19m^2-1))/(720m^3)(Delta^3f_(r-3)-Delta^3f_0)-((m^2-1)(9m^2-1))/(480m^3)(Delta^4f_(r-4)+Delta^4f_0).

Explore with Wolfram|Alpha

More things to try:

numerical summation
{1/4, -1/2, 1} cross {1/3, 1, -2/3}
gaussian blur monkey image radius x

References

Lubbock, J. W. Cambridge Philos. Trans. 3, 323, 1829.Whittaker, E. T. and Robinson, G. "Lubbock's Formula of Summation." §74 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 149-150, 1967.

Referenced on Wolfram|Alpha

Lubbock's Formula

Cite this as:

Weisstein, Eric W. "Lubbock's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LubbocksFormula.html

Lubbock's Formula

Explore with Wolfram|Alpha

References

Referenced on Wolfram|Alpha

Cite this as:

Subject classifications