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The exponential function is an E-function, in its case c n = 1 for all of the n. If λ is an algebraic number then the Bessel function J λ is an E-function. The sum or product of two E-functions is an E-function. In particular E-functions form a ring. If a is an algebraic number and f(x) is an E-function then f(ax) will be an E-function.
The exponential function can be naturally extended to a complex function, which is a function with the complex numbers as domain and codomain, such that its restriction to the reals is the above-defined exponential function, called real exponential function in what follows.
The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = () = for every b > 0.
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]
List of representations of e; Euler's identity; Exponential decay; Exponential distribution; Exponential factorial; Exponential family; Exponential formula; Exponential function; Exponential growth; Exponential integral; Exponential minus 1; Exponential sum; Exponentiation; Exponentiation by squaring
The mathematical constant e can be represented in a variety of ways as a real number.Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two integers, but it can be represented as a continued fraction.
In computer science, a math library (or maths library) is a component of a programming language's standard library containing functions (or subroutines) for the most common mathematical functions, such as trigonometry and exponentiation. Bit-twiddling and control functionalities related to floating point numbers may also be included (such as in C).