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http://functions.wolfram.com/07.23.03.abn4.01
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Hypergeometric2F1[-(15/4), 15/4, -(11/2), -z] ==
(1/(2112 Sqrt[2] Sqrt[-1 + Sqrt[1 + z]]))
(Sqrt[z] ((1056 + 2448 z + 714 z^2 - 617 z^3 + 660 z^4 - 913 z^5 -
7944 z^6 - 8208 z^7 - 2496 z^8)/(1 + z)^5 +
(1/(1 + z)^(11/2)) (2 (528 + 1488 z + 903 z^2 - 250 z^3 + 187 z^4 -
264 z^5 + 6436 z^6 + 13944 z^7 + 10080 z^8 + 2496 z^9))))
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Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["15", "4"]]], ",", FractionBox["15", "4"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2112", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]], RowBox[List["(", RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["1056", "+", RowBox[List["2448", " ", "z"]], "+", RowBox[List["714", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["617", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["660", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["913", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["7944", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8208", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["2496", " ", SuperscriptBox["z", "8"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["11", "/", "2"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["528", "+", RowBox[List["1488", " ", "z"]], "+", RowBox[List["903", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["250", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["187", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["264", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["6436", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["13944", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["10080", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["2496", " ", SuperscriptBox["z", "9"]]]]], ")"]]]]]]]], ")"]]]], ")"]]]]]]]]
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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> <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> 15 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 15 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mn> 11 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </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["15", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["15", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["11", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] </annotation> </semantics> <mo>  </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2112 </mn> <mo> ⁢ </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2496 </mn> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8208 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 7944 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 913 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 660 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 617 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 714 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2448 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1056 </mn> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 5 </mn> </msup> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 11 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2496 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 10080 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13944 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6436 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - 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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["15", "4"]]], ",", FractionBox["15", "4"], ",", RowBox[List["-", FractionBox["11", "2"]]], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["z"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["1056", "+", RowBox[List["2448", " ", "z"]], "+", RowBox[List["714", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["617", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["660", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["913", " ", SuperscriptBox["z", "5"]]], "-", RowBox[List["7944", " ", SuperscriptBox["z", "6"]]], "-", RowBox[List["8208", " ", SuperscriptBox["z", "7"]]], "-", RowBox[List["2496", " ", SuperscriptBox["z", "8"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "5"]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["528", "+", RowBox[List["1488", " ", "z"]], "+", RowBox[List["903", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["250", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["187", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["264", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["6436", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["13944", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["10080", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["2496", " ", SuperscriptBox["z", "9"]]]]], ")"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["11", "/", "2"]]]]]], ")"]]]], RowBox[List["2112", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]]]]] |
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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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