Series[ArcTan[x]^2, {x, 0, 10}]

Needs["SpecialFunctions`"]

Taylor[ArcTan[x]^2, {x, 0, 10}]

Series[ArcTan[x]^2, {x, 0, 500}]; // Timing

Taylor[ArcTan[x]^2, {x, 0, 500}]; // Timing

Series[(E^x) Cos[x], {x, 0, 20}]

Taylor[(E^x) Cos[x], {x, 0, 20}]

Series[(E^x) Cos[x], {x, 0, 500}]; // 
      Timing

Taylor[(E^x) Cos[x], {x, 0, 500}]; // 
      Timing

ps = FPS[(E^x) Cos[x], x] // Timing

ps /. {sum -> Sum, Infinity -> 500}; // Timing