Difference between revisions of "Incomplete beta function"
From specialfunctionswiki
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=Properties= | =Properties= | ||
{{:Relationship between incomplete beta and hypergeometric pfq}} | {{:Relationship between incomplete beta and hypergeometric pfq}} | ||
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| + | =References= | ||
| + | [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/page_263.htm] | ||
Revision as of 17:40, 25 July 2015
The incomplete beta function is defined by $$B_x(a,b)=\displaystyle\int_0^x t^{a-1}(1-t)^{b-1} dt.$$
Properties
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.
