# 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" enhanced   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
set yrange [ 0.00000 : 6.00000 ] noreverse
set lmargin  10
set rmargin  10
set tmargin  4
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"