Constants of e

The mathematical e constants.

Definition

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)
• e ≈ 2.71828 18284 59045 23536 02874 71352 66249 77572 47093
• 1/e ≈ 0.36787 94411 71442 32159 55237 70161 46086 74458 11131
• e² ≈ 7.38905 60989 30650 22723 04274 60575 00781 31803 15570
• M = log₁₀(e) ≈ 0.43429 44819 03251 82765 11289 18916 60508 22943 97005
• 1/M = ln(10) ≈ 2.30258 50929 94045 68401 79914 54684 36420 76011 01488
• log₁₀(M) ≈ 9.63778 43113 00536 78912 29674

Key Properties

Derivatives of e:

• (e^x)' = e^x

Integrals of e:

• ∫ e^x dx = e^x + c

Base e logarithm:

• ln(x) = log_e(x)

Exponential function:

• f(x) = exp(x) = e^x

Euler's equation:

• e^(iθ) = cos(θ) + i sin(θ)