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  2. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_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.

  3. Characterizations of the exponential function - Wikipedia

    en.wikipedia.org/wiki/Characterizations_of_the...

    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]

  4. Exponential decay - Wikipedia

    en.wikipedia.org/wiki/Exponential_decay

    A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly. This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

  5. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    The stability function of an explicit Runge–Kutta method is a polynomial, so explicit Runge–Kutta methods can never be A-stable. [32] If the method has order p, then the stability function satisfies () = + (+) as . Thus, it is of interest to study quotients of polynomials of given degrees that approximate the exponential function the best.

  6. Stretched exponential function - Wikipedia

    en.wikipedia.org/wiki/Stretched_exponential_function

    The compressed exponential function (with β > 1) has less practical importance, with the notable exceptions of β = 2, which gives the normal distribution, and of compressed exponential relaxation in the dynamics of amorphous solids. [1] In mathematics, the stretched exponential is also known as the complementary cumulative Weibull distribution.

  7. Exponential sum - Wikipedia

    en.wikipedia.org/wiki/Exponential_sum

    If the sum is of the form = ()where ƒ is a smooth function, we could use the Euler–Maclaurin formula to convert the series into an integral, plus some corrections involving derivatives of S(x), then for large values of a you could use "stationary phase" method to calculate the integral and give an approximate evaluation of the sum.

  8. Exponential response formula - Wikipedia

    en.wikipedia.org/wiki/Exponential_response_formula

    Complex replacement is used for solving differential equations when the non-homogeneous term is expressed in terms of a sinusoidal function or an exponential function, which can be converted into a complex exponential function differentiation and integration. Such complex exponential function is easier to manipulate than the original function.

  9. File:Exponential pdf.svg - Wikipedia

    en.wikipedia.org/wiki/File:Exponential_pdf.svg

    You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.

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