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

• 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.

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

• 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.

• 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.

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

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

• 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.

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

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

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

• 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.

• Fuglede's conjectureRelated: These are the functions whose orthogonality defines spectrality.