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 | | http://functions.wolfram.com/07.23.03.9531.01 | 
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 | | Hypergeometric2F1[-(23/4), 3/4, 5/2, -z] == 
 (2 Sqrt[2] (-2 (4807 + 52877 z + 57986 z^2 + 79318 z^3 + 69911 z^4 + 
      38189 z^5 + 11808 z^6 + 1584 z^7) + (1/Sqrt[1 + z]) 
     (9614 + 110561 z + 287816 z^2 + 456358 z^3 + 518810 z^4 + 391457 z^5 + 
      187784 z^6 + 51984 z^7 + 6336 z^8)))/
  (480675 z^(3/2) Sqrt[-1 + Sqrt[1 + z]]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", FractionBox["3", "4"], ",", FractionBox["5", "2"], ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["4807", "+", RowBox[List["52877", " ", "z"]], "+", RowBox[List["57986", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["79318", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["69911", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["38189", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["11808", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1584", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SqrtBox[RowBox[List["1", "+", "z"]]]], RowBox[List["(", RowBox[List["9614", "+", RowBox[List["110561", " ", "z"]], "+", RowBox[List["287816", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["456358", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["518810", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["391457", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["187784", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["51984", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["6336", " ", SuperscriptBox["z", "8"]]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["480675", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]], ")"]]]]]]]] | 
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</mo>  <mn> 1 </mn>  </mrow>  </msqrt>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mn> 2 </mn>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 6336 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 51984 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 187784 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 391457 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 518810 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 456358 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 287816 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 110561 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 9614 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 1584 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 11808 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 38189 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 69911 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 79318 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 57986 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 52877 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 4807 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 23 <sep /> 4 </cn>  </apply>  <cn type='rational'> 3 <sep /> 4 </cn>  </list>  <list>  <cn type='rational'> 5 <sep /> 2 </cn>  </list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 480675 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 3 <sep /> 2 </cn>  </apply>  <apply>  <power />  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 6336 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 51984 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 187784 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 391457 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 518810 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 456358 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 287816 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 110561 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 9614 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 1584 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 11808 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 38189 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 69911 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 79318 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 57986 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 52877 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> 4807 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["23", "4"]]], ",", FractionBox["3", "4"], ",", FractionBox["5", "2"], ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["4807", "+", RowBox[List["52877", " ", "z"]], "+", RowBox[List["57986", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["79318", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["69911", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["38189", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["11808", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["1584", " ", SuperscriptBox["z", "7"]]]]], ")"]]]], "+", FractionBox[RowBox[List["9614", "+", RowBox[List["110561", " ", "z"]], "+", RowBox[List["287816", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["456358", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["518810", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["391457", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["187784", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["51984", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["6336", " ", SuperscriptBox["z", "8"]]]]], SqrtBox[RowBox[List["1", "+", "z"]]]]]], ")"]]]], RowBox[List["480675", " ", SuperscriptBox["z", RowBox[List["3", "/", "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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