When this number is raised to the power of "pi times the square root of 163," it is shockingly close to an integer and known as Ramanujan's (rah-MAHN-uh-jahn's) constant.
This number is the base of the q term that appears twice in Dedekind's eta (DAY-duh-kind's AY-tuh) function and that is known as the "nome" in number theory. This number is the base in the in nite sum that defines Jacobi's theta function. When this number is raised to the power of "pi times the square root of 163," it is shockingly close to an integer and known as Ramanujan's (rah-MAHN-uh-jahn's) constant. In Stirling's approximation for n factorial, this number is raised to the minus n. For the limit as n goes to infinity, this number is equal to the nth power of the quantity "one plus one over n." The Taylor series for "this number to the x power" is an in nite sum, from zero, of "x to the n" over "n factorial" because the derivative of this number to the x power is still this number to the x power is still this number to the x power. For 10 points, what number, sometimes named for Euler, is approximately 2.718?
This number is the base of the q term that appears twice in Dedekind's eta (DAY-duh-kind's AY-tuh) function and that is known as the "nome" in number theory.
e [or exponential; accept Euler's number or Euler's constant before "Euler"]