Sum Floor Function Series

Sum of product of x and y such that floor n x y.

Sum floor function series.

Using series apply with a native vectorized numpy function makes no sense in most cases as it will run the numpy function in a python loop leading to much worse performance. Sum or a function aggregating over time any function ending in over time. Summation of certain series. The floor function really throws the wrench in the works.

For y fixed and x a multiple of y the fourier series given converges to y 2 rather than to x mod y 0. You could do something like this using numpy s floor for. You d be much better off using np floor series directly as suggested by several other answers. Ratio of mth and nth term in an arithmetic progression ap program to print gp geometric progression find m th summation of first n natural numbers.

0 x. This answer is wrong do not do this. The best strategy is to break up the interval of integration or summation into pieces on which the floor function is constant. Int limits 0 infty lfloor x rfloor e x dx.

Evaluate 0 x e x d x. Sum of elements of a geometric progression gp in a given range. Floor floor v instant vector. However use of this formula does quickly illustrate how functions can be represented as a power series.

To use the geometric series formula the function must be able to be put into a specific form which is often impossible. At points of discontinuity a fourier series converges to a value that is the average of its limits on the left and the right unlike the floor ceiling and fractional part functions. Definite integrals and sums involving the floor function are quite common in problems and applications. Does this infinite sum provide a new analytic continuation for zeta s.

Program to print arithmetic progression series. Solving equations with dozens of ceil and floor functions efficiently. The following functions allow aggregating each series of a given range vector over time and return an instant vector with per series aggregation results. At points of continuity the series converges to the true.