Integration sample

Calculation of the modified Bessel function K(n, x) with a non-integer index n by its integral representation.
  1. Type in the expression field:

  2. exp(-x*cosh(t)) * cosh(nu*t)
  3. Switch the Integration mode on
  4. In the corresponding entry fields enter
  5.            0 for the lower limit 
               5 for the upper limit
  6. Initialize the parameters as follows
  7.            t - mark as variable 
               x = 2 
               nu = 1.5
  8. Click the Start button.
You obtain immediately (provided you choose 7 digits precision):

Result = 0.179907
Estimated error = 1.4e-09

To verify this result, use the exact formula for the modified Bessel function of half-integer index. Input the following expression:

sqrt(PI/(2*x)) * exp(-x) * (1+1/x),

switch to the calculator mode and input the value of x:

x = 2

Then click the Start button.

You will obtain the same result:

Result = 0.179907