This number can be calculated with the infinite se
This number can be calculated with the infinite series that sums 1 over n factorial from zero to infinity or as the limit, as x goes to 0, of the quantity 1 plus x raised to the 1 over x power..  Cosine theta plus "i" sine theta is the result of raising this number to the product of i and theta, which results in the equation where this number to the power of i pi minus 1 equals zero. The function created by raising this constant to the power of x is its own derivative. For 10 points, name this awesome irrational transcendental number, the base of the natural logarithm.
This number can be calculated with the infinite series that sums 1 over n factorial from zero to infinity or as the limit, as x goes to 0, of the quantity 1 plus x raised to the 1 over x power..  
e [accept Euler’s Number, prompt on annoyingly pretentious people who try to give you “2.71828182845904523536” or some part thereof, prompt on “Napier’s” Constant, do not  accept or prompt on “Euler-Mascheroni” Number or Constant]