# expint

Exponential integral function

## Description

example

Y = expint(X) evaluates the exponential integral for each element of X.

## Examples

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Find the exponential integral for X = 1+2i.

Y = expint(1+2i)
Y = -0.1268 - 0.0351i

Plot the exponential integral for X in the interval of [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 Arguments

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Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double
Complex Number Support: Yes

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### Exponential Integral

The exponential integral of x is defined as

By analytic continuation, expint is a scalar-valued function in the complex plane cut along the negative real axis.

There is a different function that is sometimes called the exponential integral: the Cauchy principal value integral

which, for positive real x, is related to expint as

$\underset{\delta \to 0+}{\mathrm{lim}}{E}_{1}\left(-x+i0\right)=-\text{Ei}\left(x\right)-i\pi .$

## References

[1] Abramowitz, M. and I. A. Stegun. Handbook of Mathematical Functions. Chapter 5, New York: Dover Publications, 1965.

## Version History

Introduced before R2006a