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### Convergence of Newton series for sin ax

Let's define half discrete-analytic function as a function whose Newton series converges to that function for each $x>0$:
$$f(x)=\sum_{k=0}^\infty \binom{x}k \Delta^k f\left ...

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### Convergence of a Trigonometric Series

After working with a Fourier series for a while, I realized that it would be of great help to me if I could prove that the following limit is zero:
$$\lim_{N\to\infty}_{N\in ...

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### Where the following interpolation method converges?

In this question about discrete-analytic functions (that is functions, who equal to their Newton series) I asked for a solution for the following problem:
Is there a method to extend the notion ...