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 | | http://functions.wolfram.com/07.23.20.0007.01 | 
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 | | D[Hypergeometric2F1[a, b, a + 1, z], a] == 
 ((z b)/(a + 1)^2) HypergeometricPFQ[{a + 1, a + 1, b + 1}, {a + 2, a + 2}, z] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["D", "[", RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", "b", ",", RowBox[List["a", "+", "1"]], ",", "z"]], "]"]], ",", "a"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["z", " ", "b"]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "1"]], ")"]], "2"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["a", "+", "1"]], ",", RowBox[List["b", "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["a", "+", "2"]], ",", RowBox[List["a", "+", "2"]]]], "}"]], ",", "z"]], "]"]]]]]]]] | 
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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>  <mo> ∂ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> a </mi>  <mo> , </mo>  <mi> b </mi>  </mrow>  <mo> ; </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["b", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  </mrow>  <mrow>  <mo> ∂ </mo>  <mi> a </mi>  </mrow>  </mfrac>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mfrac>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 3 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["b", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <partialdiff />  <bvar>  <ci> a </ci>  </bvar>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <ci> a </ci>  <ci> b </ci>  </list>  <list>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <plus />  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  <list>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["a_"]]], RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", RowBox[List["a_", "+", "1"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["z", " ", "b"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List["a", "+", "1"]], ",", RowBox[List["b", "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["a", "+", "2"]], ",", RowBox[List["a", "+", "2"]]]], "}"]], ",", "z"]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "1"]], ")"]], "2"]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | HypergeometricPFQ[{},{},z] |  | HypergeometricPFQ[{},{b},z] |  | HypergeometricPFQ[{a},{},z] |  | HypergeometricPFQ[{a},{b},z] |  | HypergeometricPFQ[{a1},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] |  | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] |  | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] |  |  | 
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