Hello All,

If you look in your HP-65 and HP-67 Math Pac manuals and the HP-41 High Level Math solution book, you may come across programs that calculate the Jn(x) and In(x) Bessel functions. These programs use recursive algorithms that calculate series of a specified number of terms m. The documentation calculates m using an interesting formula:

m = 2 * INT[(6 + max(n,z) + 9z/(z + 2))/2]

Where n is the order of the Bessel function and z = 3x/2.

My question, can anyone find the reference for HP's algorithms to calculate the Jn(x) and In(x) Bessel functions using the above equation?? The HP documentation mentions the "Handbook of Mathematical Functions" by Abramowitz et al. as a reference. I looked in that book and and the closest thing I found was at the bottom of page 385 (under the heading Numerical Methods). The handbook discusses informally the algorithm HP used but does not mention m and how it is calculated. Did I miss something? Or is the equation for m something HP came up with?

I guess you can say that this is a math challenge, with a new twist!

Namir

*Edited: 3 Nov 2009, 4:20 p.m. *