# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'elliptic.1.png'
set border 3 front lt black linewidth 1.000 dashtype solid
set format x "%.1f" 
set key title "Π(n,k) = {/*2 ∫@_{/*0.5 0}^{/*.5 π/2}}{/:Italic [1-nsin^2(t)]^{-1} sqrt(1-k^2sin^2(t))^{-1} dt}\n" center
set key fixed left top vertical Left reverse enhanced autotitle nobox
set samples 250, 250
set style data lines
set xtics border in scale 1,0.5 nomirror norotate  autojustify
set xtics  norangelimit 0.1 
set ytics border in scale 1,0.5 nomirror norotate  autojustify
set ytics  norangelimit 1 
set title "Complete elliptic integral of the third kind EllipticPi(n,k)" 
set xlabel "{/:Italic k}" 
set xrange [ 0.00000 : 1.00000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ 0.00000 : 6.00000 ] noreverse nowriteback
set y2range [ * : * ] noreverse writeback
set zrange [ * : * ] noreverse writeback
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set lmargin  10
set rmargin  10
set tmargin  4
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
NO_ANIMATION = 1
save_encoding = "utf8"
plot EllipticPi(0.5,x) with lines lw 2 title "n = 0.5",      EllipticPi(0.0,x) with lines lw 2 title "n = 0",      EllipticPi(-1.,x) with lines lw 2 title "n = -1",      EllipticPi(-3.,x) with lines lw 2 title "n = -3",      EllipticPi(-10.,x) with lines lw 2 lc "brown" title "n = -10"