Month: February 2019

At first, we sample in the ( is odd) equidistant points around : [ f_k = f(x_k),: x_k = x^*+kh,: k=-frac{N-1}{2},dots,frac{N-1}{2} ] where is some step. Then we interpolate points by polynomial begin{equation} label{eq:poly} P_{N-1}(x)=sum_{j=0}^{N-1}{a_jx^j} end{equation} Its coefficients are found as a solution of system of linear equations: begin{equation} label{eq:sys} left{ P_{N-1}(x_k) = f_kright},quad k=-frac{N-1}{2},dots,frac{N-1}{2}…
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Let be a positive integer and let denote the fractional part function, then calculate in closed-form the following Triple Integral : ∫01∫01∫01lnk(xyz)\bigg{\bigg(xy\bigg)k\bigg}\bigg{\bigg(yz\bigg)k\bigg}\bigg{\bigg(zx\bigg)k\bigg}dx dy dz\int_{0}^{1}\int_{0}^{1}\int_{0}^{1}\ln^k(xyz)\bigg\{\bigg(\frac{x}{y}\bigg)^k\bigg\}\bigg\{\bigg(\frac{y}{z}\bigg)^k\bigg\}\bigg\{\bigg(\frac{z}{x}\bigg)^k\bigg\}\mathrm dx\ \mathrm dy\ \mathrm dz