e constant or Euler's number is a mathematical constant. The e constant is real and irrational number.
e = 2.718281828459...
- Definition of e
- Properties of e
- Base e logarithm
- Exponential function
- Euler's formula
The e constant is defined as the limit:
The e constant is defined as the limit:
The e constant is defined as the infinite series:
The reciprocal of e is the limit:
The derivative of the exponential function is the exponential function:
(e x)' = ex
The derivative of the natural logarithm function is the reciprocal function:
(loge x)' = (ln x)' = 1/x
The indefinite integral of the exponential function ex is the exponential function ex.
∫ ex dx = ex+c
The indefinite integral of the natural logarithm function loge x is:
∫ loge x dx = ∫ lnx dx = x ln x - x +c
The definite integral from 1 to e of the reciprocal function 1/x is 1:
The natural logarithm of a number x is defined as the base e logarithm of x:
ln x = loge x
The exponential function is defined as:
f (x) = exp(x) = ex
The complex number e iθ has the identity:
eiθ = cos(θ) + i sin(θ)
i is the imaginary unit (the square root of -1).
θ is any real number.
Answers to Questions (FAQ)
How to find a number in e?
Finding a number indigits necessitates to browse all its decimals, there is no other mean. There are no mean to predict a number and its position in .
What are the names for e?
is also called Euler's number or Napier's constant.
How many digits are there in e decimals?
There are an infinite number of decimal places in the number e=2.71828... Supercomputers are continuing to find more. dCode knows thedecimals until 1000000 (one million digits of e).
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