Linked from

The 52 pages that link to Exponential function, each with the reason it gives.

• PolynomialCompared with: Polynomial variables occur in bases with fixed integer exponents, not exponents.

• FunctionBroader topic: It models growth or decay at a rate proportional to the current amount.

• LogarithmCompared with: Logarithms reverse this operation, recovering the exponent from the function's output.

• FactorialCompared with: Its series uses factorials while its growth is far slower than factorial growth.

• ExponentiationBroader topic: It turns exponentiation into a continuous model of changing quantities.

• Exponential growthBroader topic: Its curve describes quantities that change by equal proportions over equal intervals.

• Periodic functionCompared with: Real exponentials generally grow or decay instead of repeating at fixed intervals.

• Euler's formulaRelated: Replacing its real input with iθ gives the left side of the identity.

• Trigonometric functionsRelated: Complex exponentials generate sine and cosine through Euler's formula.

• Complex exponentialNarrower topic: The complex exponential extends this familiar function from real inputs to the complex plane.

• Laplace transformRelated: Exponential functions form the kernel that weights values in the transform integral.

• Logarithmic scaleCompared with: It reverses logarithmic compression by turning equal input steps into equal output ratios.

• Natural logarithmCompared with: It reverses the natural logarithm: ln(eˣ) = x.

• CodomainBroader topic: Over the real numbers, its positive outputs make the choice of codomain consequential.

• Matrix exponentialCompared with: The scalar addition law generally fails for matrices that do not commute.

• Exponential decayNarrower topic: Decay follows this function when the proportional rate is constant.

• Ratio testRelated: Its factorial denominators make the ratio test yield convergence for every real input.

• Geometric progressionRelated: At integer indices, an exponential function can generate a geometric progression.

• Gaussian functionNarrower topic: A Gaussian is built by applying an exponential to a negative quadratic.

• Polynomial functionCompared with: Its variable exponent produces growth behavior unlike the fixed integer powers of a polynomial.

• PowerRelated: A fixed base turns powers into a function that models proportional growth or decay.

• AntiderivativeRelated: Its natural-base form is an antiderivative of itself.

• Chernoff boundRelated: Exponentiating deviations makes moment information yield exponentially decaying estimates.

• Euler's identityRelated: The identity uses the exponential function with a complex exponent.

• Euler's NumberRelated: The function eˣ is uniquely unchanged by differentiation.

• Hyperbolic functionsRelated: The exponential definitions of hyperbolic sine and cosine produce the whole family.

• Johann BernoulliRelated: Johann investigated exponential curves and their role in solving mathematical problems.

• Root testRelated: The test readily detects geometric-scale decay and growth in exponential terms.

• Slide ruleRelated: Exponential scales support powers and roots without repeated multiplication.

• Cauchy productRelated: Its power series coefficients multiply by the Cauchy rule to recover the addition identity.

• Charles HermiteRelated: The constant whose transcendence Hermite proved is the exponential function’s natural base.

• Gaussian integralNarrower topic: Exponential decay makes the integrand rapidly approach zero as |x| grows.

• Weierstrass factorization theoremRelated: The exponential of an entire function supplies the factor invisible to the zero set.

• Common logarithmCompared with: The base-10 exponential function reverses the operation of taking a common logarithm.

• Exponential generating functionRelated: Its coefficients illustrate the factorial weighting in the simplest exponential generating function.

• Linear functionCompared with: Its constant multiplicative growth contrasts with a linear function’s constant additive change.

• Logistic functionRelated: The logistic function is built from an exponential term and approaches it at one tail.

• Bernoulli's inequalityRelated: Taking powers with exponent n and increment x/n connects the inequality to exponential growth bounds.

• Quadratic functionCompared with: Exponential growth is not polynomial growth and does not produce a parabolic graph.

• Grönwall's inequalityRelated: The inequality's exponential bound reflects how a proportional growth limit accumulates over time.

• Lambert W functionNarrower topic: Multiplying this function by its input creates the map that Lambert W inverts.

• Logarithmic differentiationRelated: Exponentials and logarithms are inverse functions, linking variable powers to logarithmic derivatives.

• Range of a functionBroader topic: Its outputs are positive, but zero is approached rather than attained.

• Elementary algebraBroader topic: Exponential models describe repeated proportional growth and decay.

• Elementary functionBroader topic: Exponentials are one of the defining function families in the construction.

• Karamata's inequalityRelated: Applying Karamata to this convex function bounds exponential sums under majorization.

• Hyperbolic angleNarrower topic: The formulas cosh t = (eᵗ + e⁻ᵗ)/2 and sinh t = (eᵗ − e⁻ᵗ)/2 define the parameter’s coordinates.

• Inverse hyperbolic functionsNarrower topic: Hyperbolic functions and their inverses reduce to expressions involving exponentials.

• NeperRelated: Exponentiating a neper value recovers the corresponding field-quantity ratio.

• Differentiation rulesRelated: Its derivative is especially simple for the natural base and follows by composition for other bases.