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・ Exponential integral
・ Exponential integrate-and-fire
・ Exponential integrator
・ Exponential map
・ Exponential map (discrete dynamical systems)
・ Exponential map (Lie theory)
・ Exponential map (Riemannian geometry)
・ Exponential mechanism (differential privacy)
・ Exponential object
・ Exponential polynomial
・ Exponential random graph models
・ Exponential search
・ Exponential sheaf sequence
・ Exponential smoothing
・ Exponential stability
Exponential sum
・ Exponential Technology
・ Exponential time hypothesis
・ Exponential tree
・ Exponential type
・ Exponential utility
・ Exponential-Golomb coding
・ Exponential-logarithmic distribution
・ Exponentially closed field
・ Exponentially equivalent measures
・ Exponentially modified Gaussian distribution
・ Exponentiated Weibull distribution
・ Exponentiation
・ Exponentiation by squaring
・ Exponerad


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Exponential sum : ウィキペディア英語版
Exponential sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function
:e(x) = \exp(2\pi ix).\,
Therefore a typical exponential sum may take the form
:\sum_n e(x_n),
summed over a finite sequence of real numbers ''x''''n''.
==Formulation==

If we allow some real coefficients ''a''''n'', to get the form
:\sum_n a_n e(x_n)
it is the same as allowing exponents that are complex numbers. Both forms are certainly useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in diophantine approximation.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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