//@version=4
study("Simplified T3 Lines", shorttitle="T3 Lines", overlay=true)
// T3 Fast Line
aLength = input(5, minval=1, title="Fast T3 Length")
AxPrice = close
axe1 = ema(AxPrice, aLength)
axe2 = ema(axe1, aLength)
axe3 = ema(axe2, aLength)
axe4 = ema(axe3, aLength)
axe5 = ema(axe4, aLength)
axe6 = ema(axe5, aLength)
ab = 0.7
ac1 = -ab * ab * ab
ac2 = 3 * ab * ab + 3 * ab * ab * ab
ac3 = -6 * ab * ab - 3 * ab - 3 * ab * ab * ab
ac4 = 1 + 3 * ab + ab * ab * ab + 3 * ab * ab
fastT3 = ac1 * axe6 + ac2 * axe5 + ac3 * axe4 + ac4 * axe3
// T3 Slow Line
Length = input(8, minval=1, title="Slow T3 Length")
xPrice = close
xe1 = ema(xPrice, Length)
xe2 = ema(xe1, Length)
xe3 = ema(xe2, Length)
xe4 = ema(xe3, Length)
xe5 = ema(xe4, Length)
xe6 = ema(xe5, Length)
b = 0.7
c1 = -b * b * b
c2 = 3 * b * b + 3 * b * b * b
c3 = -6 * b * b - 3 * b - 3 * b * b * b
c4 = 1 + 3 * b + b * b * b + 3 * b * b
slowT3 = c1 * xe6 + c2 * xe5 + c3 * xe4 + c4 * xe3
// Plotting T3 Lines
plot(fastT3, color=color.green, title="T3 Fast Line", linewidth=2)
plot(slowT3, color=color.red, title="T3 Slow Line", linewidth=2)