Difference between revisions of "Bessel polynomial generalized hypergeometric"

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<strong>[[Bessel polynomial generalized hypergeometric|Theorem]]:</strong> The following formula holds:
 
<strong>[[Bessel polynomial generalized hypergeometric|Theorem]]:</strong> The following formula holds:
 
$$y_n(x)={}_2F_0 \left( -n, 1+n;-; -\dfrac{1}{2}x \right),$$
 
$$y_n(x)={}_2F_0 \left( -n, 1+n;-; -\dfrac{1}{2}x \right),$$
where $y_n(x)$ denotes a [[Bessel polynomial]] and ${}_2F_0$ denotes the [[hypergeometric pfq|generalized hypergeometric function]].
+
where $y_n(x)$ denotes a [[Bessel polynomial]] and ${}_2F_0$ denotes the [[Hypergeometric pFq|generalized hypergeometric function]].
 
<div class="mw-collapsible-content">
 
<div class="mw-collapsible-content">
 
<strong>Proof:</strong> █  
 
<strong>Proof:</strong> █  
 
</div>
 
</div>
 
</div>
 
</div>

Revision as of 10:17, 23 March 2015

Theorem: The following formula holds: $$y_n(x)={}_2F_0 \left( -n, 1+n;-; -\dfrac{1}{2}x \right),$$ where $y_n(x)$ denotes a Bessel polynomial and ${}_2F_0$ denotes the generalized hypergeometric function.

Proof: