# 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 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
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
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) = (x<y)?int2(x,y,(y-x)/ceil((y-x)/delta)):                         -int2(y,x,(x-y)/ceil((x-y)/delta))
int2(x,y,d) = (x>y-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)
NO_ANIMATION = 1
delta = 0.2
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)"