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 | | http://functions.wolfram.com/06.20.20.0004.01 | 
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 | | D[Beta[Subscript[z, 1], Subscript[z, 2], a, b], {Subscript[z, 2], 2}] == 
 (1 - Subscript[z, 2])^(-2 + b) Subscript[z, 2]^(-2 + a) 
  (a - 1 - (a + b - 2) Subscript[z, 2]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List[SubscriptBox["z", "2"], ",", "2"]], "}"]]], RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"], ",", "a", ",", "b"]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["z", "2"]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "+", "b"]]], " ", SubsuperscriptBox["z", "2", RowBox[List[RowBox[List["-", "2"]], "+", "a"]]], " ", RowBox[List["(", RowBox[List["a", "-", "1", "-", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "2"]], ")"]], " ", SubscriptBox["z", "2"]]]]], ")"]]]]]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mfrac>  <mrow>  <msup>  <mo> ∂ </mo>  <mn> 2 </mn>  </msup>  <mrow>  <semantics>  <mi> Β </mi>  <annotation-xml encoding='MathML-Content'>  <ci> Beta </ci>  </annotation-xml>  </semantics>  <mo> ( </mo>  <mrow>  <msub>  <mi> z </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  <mo> , </mo>  <mi> a </mi>  <mo> , </mo>  <mi> b </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mo> ∂ </mo>  <msubsup>  <mi> z </mi>  <mn> 2 </mn>  <mn> 2 </mn>  </msubsup>  </mrow>  </mfrac>  <mo> ⩵ </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msubsup>  <mi> z </mi>  <mn> 2 </mn>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  </msubsup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> b </mi>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> D </ci>  <apply>  <ci> Beta </ci>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <ci> a </ci>  <ci> b </ci>  </apply>  <list>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> 2 </cn>  </list>  </apply>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> -2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> -2 </cn>  </apply>  </apply>  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <ci> b </ci>  <cn type='integer'> -2 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z_", "2"], ",", "2"]], "}"]]]]], RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"], ",", "a_", ",", "b_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["zz", "2"]]], ")"]], RowBox[List[RowBox[List["-", "2"]], "+", "b"]]], " ", SubsuperscriptBox["zz", "2", RowBox[List[RowBox[List["-", "2"]], "+", "a"]]], " ", RowBox[List["(", RowBox[List["a", "-", "1", "-", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "-", "2"]], ")"]], " ", SubscriptBox["zz", "2"]]]]], ")"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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