bessel
09-06-2009, 02:03 PM
Hello.
I' m using NR for sometime now. I would like to calculate high order cross products of bessel functions i.e., Jn(a)*Yn(b)-Jn(b)*Yn(a), where n is the order of the function and a, b the arguments.
These cross products cannot be calculated directly for high order functions as Yn(x) goes almost to infinity. In theory one could use the recurrent relations presented in "Abramowitz and Stegun: Handbook of Mathematical Functions". However in practice these expressions suffer form significantly high rounding errors, that cannot be tolerated after a couple of iterations.
Moreover for relatively small arguments, lets say in the region [0, 100], high order cross products (n>300) exceed computer limits, even if they are calculated directly.
Concluding I would like to ask, if someone has to propose an effective technique to calculate these high-order cross products.
I' m using NR for sometime now. I would like to calculate high order cross products of bessel functions i.e., Jn(a)*Yn(b)-Jn(b)*Yn(a), where n is the order of the function and a, b the arguments.
These cross products cannot be calculated directly for high order functions as Yn(x) goes almost to infinity. In theory one could use the recurrent relations presented in "Abramowitz and Stegun: Handbook of Mathematical Functions". However in practice these expressions suffer form significantly high rounding errors, that cannot be tolerated after a couple of iterations.
Moreover for relatively small arguments, lets say in the region [0, 100], high order cross products (n>300) exceed computer limits, even if they are calculated directly.
Concluding I would like to ask, if someone has to propose an effective technique to calculate these high-order cross products.