Difference between revisions of "Relationship between incomplete beta and hypergeometric 2F1"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | 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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==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.
