Sum Floor Function Series

The second moment of a sum of floor functions.

Sum floor function series.

Int limits 0 infty lfloor x rfloor e x dx. Does this infinite sum provide a new analytic continuation for zeta s. To use the geometric series formula the function must be able to be put into a specific form which is often impossible. Program to print arithmetic progression series.

However use of this formula does quickly illustrate how functions can be represented as a power series. At points of continuity the series converges to the true. Summation of certain series. Sum of product of x and y such that floor n x y.

The floor function really throws the wrench in the works. Floor floor v instant vector. In this section we discuss how the formula for a convergent geometric series can be used to represent some functions as power series. Sum of elements of a geometric progression gp in a given range.

You could do something like this using numpy s floor for. The best strategy is to break up the interval of integration or summation into pieces on which the floor function is constant. For y fixed and x a multiple of y the fourier series given converges to y 2 rather than to x mod y 0. Solving equations with dozens of ceil and floor functions efficiently.

0 x. This answer is wrong do not do this. 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. Evaluate 0 x e x d x.

Sum or a function aggregating over time any function ending in over time. 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. You d be much better off using np floor series directly as suggested by several other answers. 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.