MathMate Information
Summation sample
Calculation of the modified Bessel function I(n, x) with a non-integer
index n by its series representation.
1. Type in the expression field:
(x/2)^(2*m + nu) / ( Gam(m+1) * Gam(m+nu+1) )
2. Switch to Summation mode
3. In the corresponding entry fields enter
0 for the lower limit
10 for the upper limit
4. Initialize the parameters as follows
m - mark as variable
x = 2
nu = 1.5
5. Click the Start button.
You obtain immediately:
Result = 1.09947
To verify this result, let us use the exact formula for the modified
Bessel function of the half-integer index. Input the following
expression:
sqrt(2*x/PI) * ( -sinh(x)/x^2 + cosh(x)/x ),
then switch to calculator mode, input the value of x:
x = 2
and click the Start button.
You will obtain the same result:
Result = 1.09947