Texas Instruments TI-89 Tip List page 273

endif
EndFunc
I ported this algorithm, from Numerical Recipes in Fortran, to TI Basic. The input argument must be
greater than zero, and error message strings may be returned. You can check for this condition by
using getType() on the result.
This table shows some results for the original example problem.
Method
-ei(3.724)
á(ℯ^(-x))/x,x,-3.724,∞)
nInt(ℯ^(-x))/x,x,-3.724,∞)
nInt(ℯ^(-x))/x,x,-3.724,0) +
nInt(ℯ^(-x))/x,x,0,∞)
It is interesting that the built-in
perhaps because it symbolically finds the singularity at x = 0, and integrates over two ranges divided at
x = 0. Circumstantial evidence for this supposition is provided by that fourth method, which manually
uses nInt() over the two ranges, and returns the same result as
Bhuvanesh Bhatt has also written a function for Ei(x), and you can get it at
http://tiger.towson.edu/~bbhatt1/ti/
This is a C function called ExpIntEi(), found in his C Special Functions package. You will need the
usual hacks to use this as a true function on HW2 calculators; see the site for details.
For more information on the exponential integral, try
Handbook of Mathematical Functions, Milton Abramowitz and Irene A. Stegun, Dover, 1965. Section 5
describes and defines Ei(x), as well as its related integrals and interrelations. I used the table of
numerical values to test ei(x).
Atlas for Computing Mathematical Functions, William J. Thompson, Wiley-Interscience, 1997.
Thompson calls Ei(x) the 'exponential integral of the second kind', and coverage begins in section
5.1.2. You can often get this book inexpensively from the bookseller Edward R. Hamilton, at
http://www.hamiltonbook.com/
As mentioned, the algorithm for ei(x) comes from
Numerical Recipes in Fortran, 2e, William H. Press et al, Cambridge University Press, 1992. Section
6.3 covers the exponential integrals. This book is available on-line at http://www.nr.com.
You can also use ei(x) to find values for the logarithmic integral li(x):
x > 1
since li(x) = Ei(ln(x))
Result
-16.2252 9269 7647
-16.2967 8867 2016
-13.5159 0839 6945
-16.2967 8867 2016
á()
function is slightly more accurate that the purely numerical nInt(),
Correct Execution
significant digits
About 11
2
1
2
á()
.
time
2 sec
134 sec
53 sec
56 sec
6 - 115