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