Hi all,I want to use matlab to calculate the exponential integral,I know that the official function ExpIntegralE in Mathematica can calculate it.

As shown in the title, I want to find a relatively authoritative code to calculate exponential integral

Answer 1

[Paul]

ExpIntegralE in Mathematica seems to be the same as the two-argument form of expint in the Symbolic Math Toolbox.

[Paul]

"there is no official matlab function that is used like expint(n,x), in matlab "

Using the function at the doc page for expint linked above in this Answer

expint(sym(3),sym(5.5))

ans = 

Get the decimal representation

vpa(expint(sym(3),sym(5.5)))

ans = 

0.00049877076767550924005965009248623

which is the same result using ExpIntegalE in Mathematica link

[ma Jack]

Sorry guys, you're right, forgive my carelessness

Answer 2

[John D'Errico]

Is there a reason why you would not just use expint?

help expint

 EXPINT Exponential integral function.
    Y = EXPINT(X) is the exponential integral function for each
    element of X.  The exponential integral is defined as:
 
    EXPINT(x) = integral from x to Inf of (exp(-t)/t) dt, for x > 0.
    
    By analytic continuation, EXPINT is a scalar-valued function in
    the complex plane cut along the negative real axis.
 
    Another common definition of the exponential integral function is
    the Cauchy principal value integral from -Inf to X of (exp(t)/t)
    dt, for positive X.  This is denoted as Ei(x). The relationships
    between EXPINT(x) and Ei(x) are as follows:
 
        EXPINT(-x+i*0) = -Ei(x) - i*pi, for real x > 0
        Ei(x) = REAL(-EXPINT(-x)), for real x > 0
 
    Class support for input X:
       float: double, single

    Documentation for expint
       doc expint

    Other functions named expint

       codistributed/expint    gpuArray/expint    sym/expint

Probably you did not look for it. And that was what you did wrong. When you don't know how to do something in MATLAB, LEARN TO USE LOOKFOR. In my case, this identified many possible things, but do you see the 6th item on the list?

lookfor exponential

expmdemo1                      - Matrix exponential via Pade approximation.
expmdemo2                      - Matrix exponential via Taylor series.
expmdemo3                      - Matrix exponential via eigenvalues and eigenvectors.
exp                            - Exponential.
expm                           - Matrix exponential.
expint                         - Exponential integral function.
...

Any guesses what expint would do? The point is, USE LOOKFOR.

[ma Jack]

Sorry sir, I actually know this official matlab function, but I want to calculate exponential integrals of order p, but this function only seems to calculate exponential integrals of the first order.

[ma Jack]

Sorry, I just learned that there is a recursive relational formula to calculate exponential integrals of other orders, and this recursive formula seems very simple, so my doubt is why matlab doesn't officially release a function that directly calculates n-th exponential integrals?

Is there some complicated condition of use here? I am concerned that the result of the nth order exponential integral obtained by directly following the recursive formula and the EXPINT function is wrong in some cases. So that's what I'm really worried about

[Paul]

What is the definiton of the exponential integral of order p?

[John D'Errico]

help sym/expint

 EXPINT   Exponential integral function.
    Y = EXPINT(N,X) is the 2-argument version of the exponential
    integral. It is defined as:
 
       EXPINT(n,x) = integral from 1 to Inf of exp(-x*t)/t^n dt
 
    The function EXPINT can also be called with 1 argument.
 
    Y = EXPINT(X) is the exponential integral function. The
    exponential integral is defined as:
 
       EXPINT(x) = integral from x to Inf of (exp(-t)/t) dt,
 
    for x > 0. By analytic continuation, EXPINT is a scalar-valued
    function in the complex plane.
 
    See also EXPINT, SYM/EI.

[ma Jack]

In fact, there is no official matlab function that is used like expint(n,x), in matlab it can only be expint(x), which is equivalent to ExpIntegralE[1, x] in mathematica, but what I want is ExpIntegralE[n, x]

[Walter Roberson]

https://www.mathworks.com/help/symbolic/expint.html is not part of MATLAB???