Difference between revisions of "Modified Bessel I"

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[[Relationship between Bessel I sub n and Bessel J sub n]]<br />
 
[[Relationship between Bessel I sub n and Bessel J sub n]]<br />
 
[[Relationship between Airy Bi and modified Bessel I]]<br />
 
[[Relationship between Airy Bi and modified Bessel I]]<br />
<div class="toccolours mw-collapsible mw-collapsed">
 
<strong>Proposition:</strong> The following formula holds:
 
$$I_{\nu}(z)=\displaystyle\sum_{k=0}^{\infty} J_{\nu+k}(z) \dfrac{z^k}{k!},$$
 
where $J_{\nu}$ denotes the [[Bessel J sub nu|Bessel function of the first kind]].
 
<div class="mw-collapsible-content">
 
<strong>Proof:</strong> █
 
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</div>
 
 
 
  
 
<center>{{:Bessel functions footer}}</center>
 
<center>{{:Bessel functions footer}}</center>

Revision as of 20:12, 9 June 2016

The modified Bessel function of the first kind is defined by $$I_{\nu}(z)=i^{-\nu}J_{\nu}(iz),$$ where $J_{\nu}$ is the Bessel function of the first kind.

Properties

Relationship between Bessel I sub -1/2 and cosh
Relationship between Bessel I sub 1/2 and sinh
Relationship between Bessel I sub n and Bessel J sub n
Relationship between Airy Bi and modified Bessel I

<center>Bessel functions
</center>

References

[1]