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Program 1
Bessel Function
Output 1
Program 2
Bessel Function
1. Recurrence Relation: We verify the relation Jv-1(x) + Jv+1(x) = (2v/x) Jv(x).
2. LHS and RHS: The left-hand side (LHS) is computed as Jv-1(x) + Jv+1(x), and the right-hand side (RHS) is (2v/x) Jv(x).
3. Plot: Both sides are plotted for visual comparison.
4. Difference: The maximum difference between LHS and RHS is calculated to confirm the accuracy of the relation.
Output 2
Program 3
Bessel Function
Recurrence Relation of Bessel's Function
$$ z \frac{d}{dz} J_n(z) + n J_n(z) = z J_{n-1}(z) $$
Output 3