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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')

Figure contains an axes. The axes with title Exponential Integral contains an object of type line.

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

More About

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Exponential Integral

The exponential integral of x is defined as

E1(x)=xet/t dt.

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

Ei(x)=xet/t dt,

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

limδ0+E1(x+i0)=Ei(x)iπ.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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Introduced before R2006a