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Exponential integral function
Y = expint(X)
example
Y = expint(X) evaluates the exponential integral for each element of X.
Y
X
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Find the exponential integral for X = 1+2i.
=
1+2i
Y = expint(1+2i)
Y = -0.1268 - 0.0351i
Plot the exponential integral for X in the interval of [0,10].
[0,10]
X = 0:0.01:10; Y = expint(X); plot(X,Y) axis([-1 10 -0.5 4]) xlabel('$x$','interpreter','latex') ylabel('$E_1(x)$','interpreter','latex') title('Exponential Integral','interpreter','latex')
Input array, specified as a scalar, vector, matrix, or multidimensional array.
Data Types: single | double Complex Number Support: Yes
single
double
The exponential integral of x is defined as
E1(x)=∫x∞e−t/t dt.
By analytic continuation, expint is a scalar-valued function in the complex plane cut along the negative real axis.
expint
There is a different function that is sometimes called the exponential integral: the Cauchy principal value integral
Ei(x)=∫−∞xet/t dt,
which, for positive real x, is related to expint as
limδ→0+E1(−x+i0)=−Ei(x)−iπ.
[1] Abramowitz, M. and I. A. Stegun. Handbook of Mathematical Functions. Chapter 5, New York: Dover Publications, 1965.
This function fully supports tall arrays. For more information, see Tall Arrays.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).
exp | integral
exp
integral
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