Difference between revisions of "Relationship between Bessel I and Bessel J"
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| − | + | ==Theorem== | |
| − | + | 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 sub nu|Bessel function of the first kind]]. | where $I_n$ denotes the [[modified Bessel I sub nu|modified Bessel $I$]] and $J_n$ denotes the [[Bessel J sub nu|Bessel function of the first kind]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 19:57, 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.
