Difference between revisions of "Bessel at -n-1/2 in terms of Bessel polynomial"
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Revision as of 10:21, 23 March 2015
Theorem: The following formula holds: $$J_{-n-\frac{1}{2}}(r) = (2 \pi r)^{-\frac{1}{2}} \left[ i^n e^{ir} y_n \left( -\dfrac{1}{ir} \right)+ \dfrac{e^{-ir}}{i^n} y_n\left( \dfrac{1}{ir} \right) \right],$$ where $J_{-n-\frac{1}{2}}$ denotes a Bessel function and $y_n$ denotes a Bessel polynomial.
Proof: █