|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.23.03.0886.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Hypergeometric2F1[-(11/2), 1, 3, z] ==
-((1/(195 z^2)) (4 (2 - 2 Sqrt[1 - z] +
z (-15 + 14 Sqrt[1 - z] + 2 Sqrt[1 - z] z
(-21 + z (35 + z (-35 + z (21 + (-7 + z) z))))))))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "1", ",", "3", ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List["195", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "15"]], "+", RowBox[List["14", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "35"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <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> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mn> 3 </mn> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["11", "2"]]], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["3", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric2F1] </annotation> </semantics> <mo>  </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 35 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 35 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 14 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> - </mo> <mn> 15 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 195 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -7 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 21 </cn> </apply> </apply> <cn type='integer'> -35 </cn> </apply> </apply> <cn type='integer'> 35 </cn> </apply> </apply> <cn type='integer'> -21 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 14 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -15 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 195 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "1", ",", "3", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["4", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "15"]], "+", RowBox[List["14", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "21"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["35", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "35"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["21", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "7"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["195", " ", SuperscriptBox["z", "2"]]]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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] | |
|
|
|