Category

Exponentials

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[[File:Expo02.svg|thumb|Graphs of for various bases :

hyperbolic function

mathematical function related with trigonometric functions

result of multiplying a number, or other expression, by itself

Euler's identity

e ^ (πi) + 1 = 0

exponential function

mathematical function with a constant base and a variable exponent, denoted exp_a(x) or a^x

logarithmic spiral

self-similar growth spiral whose curvature pattern appears frequently in nature

radioactive decay

emission of subatomic particles by the decay of an atomic nucleus

compound interest

when interest is added to the principal of a deposit or loan, so that, from that moment on, the interest that has been added also earns interest

exponential distribution

probability distribution

exponential growth

growth of quantities at rate proportional to the current amount

thumb|right|This chain, whose ends hang from two points, forms a catenary. thumb|right|The silk on this spider web forms multiple elastic catenaries.

thumb|alt=A colorful graphic with brightly colored loops that grow in intensity as the eye goes to the right|Domain coloring of the holomorphic tetration {}^{z}e, with [[hue representing the function argument and brightness representing magnitude]] thumb|alt=A line graph with curves that bend upward dramatically as the values on the x-axis get larger|{}^{n}x, for , showing convergence to the infinitely iterated exponential between the two dots

list of integrals of exponential functions

Wikimedia list article

list of integrals of hyperbolic functions

Wikimedia list article

exponential decay

probability density

Gaussian function

mathematical function

functional relationship between two quantities, where one quantity varies as a power of another

Gudermannian function

function that relates the circular functions and hyperbolic functions without using complex numbers

exponential integral

special function defined by an integral

Lindemann–Weierstrass theorem

theorem of number theory

softmax function

function that maps a k-element real-valued vector to a k-element categorical probability distribution

matrix exponential

matrix operation generalizing exponentiation of scalar numbers

positive integer power of a prime number

zero to the power of zero

mathematical expression with no necessarily obvious value

exponentiation by squaring

wheat and chessboard problem

mathematical problem

proof that e is irrational

mathematical proof that Euler's number (e) is irrational

methods of estimating the doubling time of an investment

double exponential function

exponential function of an exponential function

Baker–Campbell–Hausdorff formula

formula in Lie theory

exponential family

probablility distribution

exponential factorial

recursive mathematical formula

exponential sum

finite sum formed using the exponential function

stretched exponential function

mathematical function common in physics

Schanuel's conjecture

conjecture concerning the transcendence degree of field extensions of the rational numbers

The term '''q-exponential''' occurs in two contexts. The q-exponential distribution, based on the Tsallis q-exponential is discussed in elsewhere.

list of representations of e

Wikimedia list article