Bessel Functions: No Common Zeros for J_n(x) and J_{n+m}(x)

Published on August 23, 2024

This proof demonstrates that Bessel functions of different orders, $J_n(x)$ and $J_{n+m}(x)$, have no common zeros except at x=0. The proof uses the Bessel differential equation, recurrence relations, and a proof by contradiction to show that assuming a common zero leads to a contradiction.

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