21. The constant of integration follows from the fact that the derivative of a constant function is 0. 22. This is similar to the fact the a constant function is one whose derivative is constantly 0. 23. It is the ( trivial ) constant function and every " x " is a root. 24. Therefore, the Lanczos interpolation of a discrete signal with constant samples does not yield a constant function . 25. The problem is that we are talking about exponentials, rather than the differentiability of a constant function . 26. Suppose is a compact Hausdorff space and is a subalgebra of which contains a non-zero constant function . 27. If U is a connected set, then the constant functions are the only antiderivatives of the zero function. 28. By standard differentiation rules, if a polynomial of degree is differentiated times, then it becomes a constant function . 29. Consequently, the kernel of \ frac { d } { dx } is the space of all constant functions . 30. The first reason is that the constant function is not normalizable, and thus is not a proper probability distribution.
