|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.23.03.0971.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Hypergeometric2F1[-(11/2), 3, -(3/2), z] ==
(1/128) (128 + 11 z (128 + 3 z (768 - 35 z (193 + 13 z (-28 + 15 z)))) +
3465 (-1 + z) z^(5/2) (21 + 13 z (-6 + 5 z)) ArcTanh[Sqrt[z]])
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "3", ",", RowBox[List["-", FractionBox["3", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "128"], " ", RowBox[List["(", RowBox[List["128", "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["128", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List["768", "-", RowBox[List["35", " ", "z", " ", RowBox[List["(", RowBox[List["193", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "28"]], "+", RowBox[List["15", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["21", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["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> 3 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <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["3", Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["3", "2"]]], 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> <mfrac> <mn> 1 </mn> <mn> 128 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3465 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 21 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 11 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 768 </mn> <mo> - </mo> <mrow> <mn> 35 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 13 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 15 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 28 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 193 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 128 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 128 </mn> </mrow> <mo> ) </mo> </mrow> </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'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 128 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3465 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <cn type='integer'> -6 </cn> </apply> </apply> <cn type='integer'> 21 </cn> </apply> <apply> <times /> <apply> <power /> <ci> tanh </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> <apply> <plus /> <cn type='integer'> 768 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> z </ci> </apply> <cn type='integer'> -28 </cn> </apply> </apply> <cn type='integer'> 193 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 128 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> 128 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", "3", ",", RowBox[List["-", FractionBox["3", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "128"], " ", RowBox[List["(", RowBox[List["128", "+", RowBox[List["11", " ", "z", " ", RowBox[List["(", RowBox[List["128", "+", RowBox[List["3", " ", "z", " ", RowBox[List["(", RowBox[List["768", "-", RowBox[List["35", " ", "z", " ", RowBox[List["(", RowBox[List["193", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "28"]], "+", RowBox[List["15", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["3465", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["(", RowBox[List["21", "+", RowBox[List["13", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "6"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTanh", "[", SqrtBox["z"], "]"]]]]]], ")"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
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] | |
|
|
|