Difference between revisions of "Relationship between incomplete beta and hypergeometric 2F1"

From specialfunctionswiki
Jump to: navigation, search
 
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed">
+
==Theorem==
<strong>[[Relationship between incomplete beta and hypergeometric pfq|Theorem]]:</strong> The following formula holds:
+
The following formula holds:
 
$$B_x(a,b)=\dfrac{x^a}{a} {}_2F_1(a,1-b;a+1;x),$$
 
$$B_x(a,b)=\dfrac{x^a}{a} {}_2F_1(a,1-b;a+1;x),$$
 
where $B_x$ denotes the [[incomplete beta function]] and ${}_2F_1$ denotes the [[hypergeometric pFq]].
 
where $B_x$ denotes the [[incomplete beta function]] and ${}_2F_1$ denotes the [[hypergeometric pFq]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong>  █
+
==Proof==
</div>
+
 
</div>
+
==References==
 +
 
 +
[[Category:Theorem]]
 +
[[Category:Unproven]]

Latest revision as of 20:26, 5 July 2016

Theorem

The following formula holds: $$B_x(a,b)=\dfrac{x^a}{a} {}_2F_1(a,1-b;a+1;x),$$ where $B_x$ denotes the incomplete beta function and ${}_2F_1$ denotes the hypergeometric pFq.

Proof

References