/sci/ - Science & Math

>>11596205
Let [math] v_1, v_2, v_3, \dots [/math] denote the values that you don't want to take the zero value and let [math] v_z [/math] be the one that should hit the zero.

Since [math] \sin(0)=0 [/math], the function
[math] f(t) := \sin(\pi \cdot \, (t-v_z)\, /\, T) [/math]
is zero at [math] t=v_z [/math].

Now you want to choose your period length [math] T [/math] such that all other [math] v_i - v_z [/math] are never an integer multiple of [math] T [/math] .

I'm trying to recall a theorem, or the name of a theorem, that can be used to express a finite sum in terms of an integral.
It can also be used to represent sums as integrals over the floor function and the like. The proof basically hints at it being a variant of the fundamental theorem of calculus.
It roughly goes like

[math] \sum_{k=1}^{n-1} A_n \phi(n) = \cdots + \int \cdot [/math]

Anybody got a hint?