expint

Exponential integral

Syntax

Y = expint(X)


Description

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

More About

Exponential Integral

The exponential integral computed by this function is defined as

$$E_1(x)={\displaystyle \underset{x}{\overset{\infty }{\int }}{e}^{-t}/tdt}$$

Another common definition of the exponential integral function is the Cauchy principal value integral

$$\text{Ei}(x)={\displaystyle \underset{-\infty }{\overset{x}{\int }}{e}^t/tdt}$$

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

$$E_1(-x)=-\text{Ei}(x)-i\pi$$

References

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

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

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

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Introduced before R2006a