Sum Floor Function Series

You d be much better off using np floor series directly as suggested by several other answers.

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. However use of this formula does quickly illustrate how functions can be represented as a power series. Sum of product of x and y such that floor n x y. 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 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. 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. Floor floor v instant vector.

For y fixed and x a multiple of y the fourier series given converges to y 2 rather than to x mod y 0. Note that when combining irate with an aggregation operator e g. The following functions allow aggregating each series of a given range vector over time and return an instant vector with per series aggregation results. Sum of elements of a geometric progression gp in a given range.

Summation of certain series. Definite integrals and sums involving the floor function are quite common in problems and applications. The second moment of a sum of floor functions. This answer is wrong do not do this.

In this section we discuss how the formula for a convergent geometric series can be used to represent some functions as 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 continuity the series converges to the true. Evaluate 0 x e x d x.

Sum or a function aggregating over time any function ending in over time. Int limits 0 infty lfloor x rfloor e x dx. Does this infinite sum provide a new analytic continuation for zeta s. 0 x.