Mathematica Floor Function Sum

Sum k n xn lfloor frac n 2 k rfloor where n is an integer and x is a small number x ll n.

Mathematica floor function sum.

Since all the functions evaluated to same value which is x. For a unit fraction 3 sums of this form lead to devil s staircase like behavior. 2 can be done analytically for rational. For instance sums of the form.

Ztransform f x z all the functions f produced the same ztransform. Inverseztransform z x x x x if the function whose ztranform you are trying to find can t be evaluated mathematica does not give a ztransform for. Changed t to tt feven to feven tt a n 4 integrate feven tt cos n tt tt 0 2. Round or the nearest integer function gives the nearest integer.

Sum f i imax evaluates the sum sum i 1 imax f. And. A 0 2 integrate feven tt tt 0 1. Browse other questions tagged real analysis number theory ceiling and floor functions or ask your own question.

X 1 π k 11 ksin 2πkx x 1 2. The floor function really throws the wrench in the works. Floor x a gives the greatest multiple of a less than or equal to x. Sum f i imin imax di uses steps d i.

One can use the fourier series representation of the floor function. F floor x ceiling x round x. Featured on meta goodbye prettify. For the rest we can verify that it gives zero contribution.

Floor or the greatest integer function gives the greatest integer less than or equal to a given value. Res 1 π sum integrate sin 2 π k x n x 0 1 k k 1 infinity 3li2 e 2inπ 3li2 e2inπ π2 12π2n. Integrate n x 1 2 x 0 1 n 2 1 2. Changed t to tt feven to feven tt fourier approximation function fapp t n a 0 sum a 2 x 1 cos 2 x 1 t x 1 n.

A number of geometric like sequences with a floor function in the numerator can be done analytically. Floor x gives the greatest integer less than or equal to x. Integrating the x 1 2 we obtain your expected answer. Sum f i imin imax j jmin jmax evaluates the multiple sum sum i imin imax sum j jmin jmax.