Constants of e

e is a mathematical constant - also called the Euler's number. e is a real and irrational number and defined as

e = lim_x→∞(1 + 1 / x)^x

   =   lim_x→∞(1 + x)^1/x

   = 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 ...                            (1)

1/e = 0.36787 94411 71442 32159 55237 70161 46086 74458 11131 ...                        (2)

e² = 7.38905 60989 30650 22723 04274 60575 00781 31803 15570 ...                         (3)

M = log₁₀(e) = 0.43429 44819 03251 82765 11289 18916 60508 22943 97005 ...                      (4)

1/M = log_e(10) = 2.30258 50929 94045 68401 79914 54684 36420 76011 01488 ...                        (5)

log₁₀(M) = 9.63778 43113 00536 78912 29674 ...                         (6)

Derivatives of e

(e^x)' = e^x                        (7)

Integrals of e

∫ e^x dx = e^x  + c                        (8)

Base e logarithm

ln(x) = log_e(x)                   (9)

Exponential function

f(x) = exp(x) = e^x                    (10)

Euler's equation

e^iθ = cos(θ) + i sin(θ)                    (11)