^ Abramowitz and Stegun, p. 228, see footnote 3.(ed.), "Asymptotic Approximations", Historical Developments in Singular Perturbations, Cham: Springer International Publishing, pp. 27–51, doi: 10.1007/978-4-3_2, ISBN 978-4-3, retrieved There have been a number of approximations for the exponential integral function. are plotted in the figure to the right with black and red curves. It is defined as one particular definite integral of the ratio between an exponential function and its argument.įor real non-zero values of x, the exponential integral Ei( x) is defined asĮi ( x ) = − ∫ − x ∞ e − t t d t = ∫ − ∞ x e t t d t. In mathematics, the exponential integral Ei is a special function on the complex plane. Plot of the exponential integral function E n(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D Not to be confused with other integrals of exponential functions.
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