AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, z, z] == Hypergeometric2F1[a, Subscript[b, 1] + Subscript[b, 2], c, z]

Cell[BoxData[RowBox[List[RowBox[List["AppellF1", "[", RowBox[List["a", ",", SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", "c", ",", "z", ",", "z"]], "]"]], "\[Equal]", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", RowBox[List[SubscriptBox["b", "1"], "+", SubscriptBox["b", "2"]]], ",", "c", ",", "z"]], "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <mi> z </mi> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> + </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;a&quot;, Hypergeometric2F1, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[SubscriptBox[&quot;b&quot;, &quot;1&quot;], &quot;+&quot;, SubscriptBox[&quot;b&quot;, &quot;2&quot;]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[&quot;c&quot;, Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric2F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> AppellF1 </ci> <ci> a </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> c </ci> <ci> z </ci> <ci> z </ci> </apply> <apply> <ci> Hypergeometric2F1 </ci> <ci> a </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> c </ci> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AppellF1", "[", RowBox[List["a_", ",", SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", "c_", ",", "z_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", RowBox[List[SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "2"]]], ",", "c", ",", "z"]], "]"]]]]]]

2001-10-29