Euler's constant

on . Posted in Algebra

The Euler's constant, abbreviated as e, also called Euler Number, is a mathematical constant that is approximately equal to 

  • \(\large{ e = lim_{n \to \infty} \left( 1 + \frac{1}{x}  \right)^x  = 2.7182818284590452353602874713527 ... }\)

Euler's constant is a transcendental number, which means it is not the root of any non-zero polynomial equation with rational coefficients.  It is the base of the natural logarithm and has many important properties in mathematics, particularly in calculus, complex analysis, and number theory.

One of the most well known properties of the constant "e" is its role in exponential functions.  The function f(x) = e^x is its own derivative, which makes it particularly useful in solving differential equations.  The constant also appears in various other mathematical contexts, such as in the study of compound interest, probability, and growth processes.

Euler's constant is an irrational number, which means it cannot be expressed as a simple fraction (ratio of two integers) and has a non-repeating, non-terminating decimal expansion.  It's a fundamental constant in mathematics and plays a crucial role in connecting different areas of mathematical study.

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Tags: Constant Geometry