@Carl Love and @acer, I would very much like to credit you for your help with the Maple evaluation. Could you send me PMs with your names so that I can credit you?

@acer , thanks very much for your time and insight. This worked well. I'll be using the version suggested in Carl Love's post above.

@Carl Love Your suggestion worked very well, I'll be using this. Thank you very much.

@Carl Love Both Pi and pi are interpreted as pi in my document. I tried both, and it made no difference to the evaluation.

@YasH You're right, the function name should be BesselJ. It made no difference to the evaluation of the expression, though.