Difference between revisions of "Relationship between Bessel I and Bessel J"
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The following formula holds: | The following formula holds: | ||
$$I_n(x)=i^{-n}J_n(ix),$$ | $$I_n(x)=i^{-n}J_n(ix),$$ | ||
| − | where $I_n$ denotes the [[modified Bessel I sub nu|modified Bessel $I$]] and $J_n$ denotes the [[Bessel J | + | where $I_n$ denotes the [[modified Bessel I sub nu|modified Bessel $I$]] and $J_n$ denotes the [[Bessel J|Bessel function of the first kind]]. |
==Proof== | ==Proof== | ||
==References== | ==References== | ||
Revision as of 20:09, 9 June 2016
Theorem
The following formula holds: $$I_n(x)=i^{-n}J_n(ix),$$ where $I_n$ denotes the modified Bessel $I$ and $J_n$ denotes the Bessel function of the first kind.
