# set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 # set output 'bivariat.8.png' set key fixed right bottom vertical Right noreverse enhanced autotitle nobox set style increment default set samples 500, 500 set style data lines set title "Finite summation of 10, 100, 1000 fourier coefficients" set xrange [ -10.0000 : 10.0000 ] noreverse writeback set x2range [ * : * ] noreverse writeback set yrange [ -0.400000 : 1.20000 ] noreverse writeback set y2range [ * : * ] noreverse writeback set zrange [ * : * ] noreverse writeback set cbrange [ * : * ] noreverse writeback set rrange [ * : * ] noreverse writeback integral_f(x) = (x>0)?int1a(x,x/ceil(x/delta)):-int1b(x,-x/ceil(-x/delta)) int1a(x,d) = (x<=d*.1) ? 0 : (int1a(x-d,d)+(f(x-d)+4*f(x-d*.5)+f(x))*d/6.) int1b(x,d) = (x>=-d*.1) ? 0 : (int1b(x+d,d)+(f(x+d)+4*f(x+d*.5)+f(x))*d/6.) f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5 integral2_f(x,y) = (xy-d*.5) ? 0 : (int2(x+d,y,d) + (f(x)+4*f(x+d*.5)+f(x+d))*d/6.) ack(m,n) = (m == 0) ? n + 1 : (n == 0) ? ack(m-1,1) : ack(m-1,ack(m,n-1)) min(x,y) = (x < y) ? x : y max(x,y) = (x > y) ? x : y gcd(x,y) = gcd1(rnd(max(x,y)),rnd(min(x,y))) rnd(x) = int(x+0.5) gcd1(x,y) = (y == 0) ? x : gcd1(y, x - x/y * y) fourier(k, x) = sin(3./2*k)/k * 2./3*cos(k*x) sum10(x) = 1./2 + sum [k=1:10] fourier(k, x) sum100(x) = 1./2 + sum [k=1:100] fourier(k, x) sum1000(x) = 1./2 + sum [k=1:1000] fourier(k, x) delta = 0.2 k = 1000 plot sum10(x) title "1./2 + sum [k=1:10] sin(3./2*k)/k * 2./3*cos(k*x)", sum100(x) title "1./2 + sum [k=1:100] sin(3./2*k)/k * 2./3*cos(k*x)", sum1000(x) title "1./2 + sum [k=1:1000] sin(3./2*k)/k * 2./3*cos(k*x)"