|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.23.03.0864.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Hypergeometric2F1[-(11/2), 1/2, 5, z] == (1/(72747675 Pi z^4))
(256
(-2 (792 + z (-8580 + z (44550 + z (-164373 +
z (-275680 + z (170022 + z (-86150 + z (30395 + 128 z (-51 +
5 z))))))))) EllipticE[z] +
(-1 + z) (-1584 +
z (16368 + z (-81213 + z (291060 + z (114770 + z (-64364 +
z (25203 + 16 z (-373 + 40 z)))))))) EllipticK[z]))
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["11", "2"]]], ",", FractionBox["1", "2"], ",", "5", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["72747675", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["792", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8580"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["44550", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "164373"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "275680"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["170022", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "86150"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30395", "+", RowBox[List["128", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "51"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1584"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["16368", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "81213"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["291060", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["114770", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "64364"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25203", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "373"]], "+", RowBox[List["40", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "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> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mn> 5 </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[FractionBox["1", "2"], Hypergeometric2F1, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["5", 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> <mrow> <mn> 72747675 </mn> <mo> ⁢ </mo> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 256 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <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> <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> <mn> 16 </mn> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 40 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 373 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 25203 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 64364 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 114770 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 291060 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 81213 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 16368 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1584 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> K </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <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> <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> <mn> 128 </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> 51 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 30395 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 86150 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 170022 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 275680 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 164373 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 44550 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 8580 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 792 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> E </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </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='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 72747675 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <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 /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> <cn type='integer'> -373 </cn> </apply> </apply> <cn type='integer'> 25203 </cn> </apply> </apply> <cn type='integer'> -64364 </cn> </apply> </apply> <cn type='integer'> 114770 </cn> </apply> </apply> <cn type='integer'> 291060 </cn> </apply> </apply> <cn type='integer'> -81213 </cn> </apply> </apply> <cn type='integer'> 16368 </cn> </apply> </apply> <cn type='integer'> -1584 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <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 /> <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 /> <cn type='integer'> 128 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> <cn type='integer'> -51 </cn> </apply> </apply> <cn type='integer'> 30395 </cn> </apply> </apply> <cn type='integer'> -86150 </cn> </apply> </apply> <cn type='integer'> 170022 </cn> </apply> </apply> <cn type='integer'> -275680 </cn> </apply> </apply> <cn type='integer'> -164373 </cn> </apply> </apply> <cn type='integer'> 44550 </cn> </apply> </apply> <cn type='integer'> -8580 </cn> </apply> </apply> <cn type='integer'> 792 </cn> </apply> <apply> <times /> <exponentiale /> <ci> z </ci> </apply> </apply> </apply> </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"]]], ",", FractionBox["1", "2"], ",", "5", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["792", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "8580"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["44550", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "164373"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "275680"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["170022", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "86150"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["30395", "+", RowBox[List["128", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "51"]], "+", RowBox[List["5", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1584"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["16368", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "81213"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["291060", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["114770", "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "64364"]], "+", RowBox[List["z", " ", RowBox[List["(", RowBox[List["25203", "+", RowBox[List["16", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "373"]], "+", RowBox[List["40", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", "z", "]"]]]]]], ")"]]]], RowBox[List["72747675", " ", "\[Pi]", " ", SuperscriptBox["z", "4"]]]]]]]] |
|
|
|
|
|
|
|
|
|
|
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] | |
|
|
|