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imAwinner
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We know that the function f(x) = sin(2*pi*x) vanishes at all integers, are there other functions like that and what is the appropriate generalization to higher dimensions?
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ZioX said:There are as many as you can draw. And more.
imAwinner said:We know that the function f(x) = sin(2*pi*x) vanishes at all integers, are there other functions like that and what is the appropriate generalization to higher dimensions?
imAwinner said:Maybe I wasn't specific, I'm looking for the formula of a function f(x,y) that would vanish at integers, could anyone help?
HallsofIvy said:If you don't think there are more than "hundreds" of such functions (or if you think of functions as limited to "formulas") then you have a very restricted idea of "function".
Functions that vanish at integers are mathematical functions that have a value of zero when the input is an integer. In other words, the function has no output or "vanishes" at whole numbers.
One example is the sine function, sin(x), which has a value of zero at all integer values of x, such as 0, 1, -2, etc.
These functions have unique properties and can be used to solve various problems in mathematics, physics, and engineering. They also provide insights into the behavior of more complex functions.
These functions can be graphed by plotting points where the input is an integer and the output is zero, and then connecting these points with a smooth curve. The resulting graph will have a series of "dips" or "peaks" at each integer value.
Yes, these functions can have non-zero values at non-integer inputs. However, their values at integer inputs will always be zero.