Project Euler formulas in Terms of Jumps withut Integration; show that for a function whose third derivative is identically zero, where n = 1, 2, ??? and we sum over all the jumps js, j's, j''s of f, f', f', respectively, located at xs.

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an 11 Π [- Σ j, sin nxs b, = mm [Σ j, by cos nxs - + Σ. j. cos nxs ἘΤ' . ] Σ;" sin nxs - Σ. j. sin n.Χ., Η Σ j cos nx. ]