>> I would like to simplify some expressions involving Bessel
>> functions using recurrences relationships like
>>
>> bessel_j(nu-1,z)+bessel_j(nu+1,z) = (2*nu/z) * bessel_j(nu,z)
>> bessel_y(nu-1,z)+bessel_y(nu+1,z) = (2*nu/z) * bessel_y(nu,z)
>
> Could you give some examples of the expressions you're starting with and
> how you'd like to use these relations to simplify them?
After substituting a solution into a differential equation I have the
following expression that should equal zero.
2 2 2
1 x 9 x 1 x
(D6) (((BESSEL_J(- -, --) + BESSEL_J(- -, --)) %C + BESSEL_J(-, --)
4 2 4 2 4 2
2 2 2
7 x 2 5 x 3 x
+ BESSEL_J(- -, --)) x + 5 BESSEL_J(- -, --) %C + 3 BESSEL_J(- -, --))
4 2 4 2 4 2
2 2
1 x 1 x
/(BESSEL_J(- -, --) %C + BESSEL_J(-, --))
4 2 4 2
Using the first relationship twice, all the terms in numerator cancel.