| |  
 |  | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | http://functions.wolfram.com/07.23.03.cbwn.01 | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Hypergeometric2F1[4, 43/8, 6, -z] == (1/(39501 z^5 (1 + z)^(27/8))) 
  (256 (384 z^4 (1 + z)^(3/8) + z^3 (5985 - 2944 (1 + z)^(3/8)) - 
    4096 (-1 + (1 + z)^(3/8)) - 384 z (-35 + 31 (1 + z)^(3/8)) - 
    48 z^2 (-315 + 232 (1 + z)^(3/8)))) | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["4", ",", FractionBox["43", "8"], ",", "6", ",", RowBox[List["-", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["39501", " ", SuperscriptBox["z", "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["27", "/", "8"]]]]]], RowBox[List["(", RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["384", " ", SuperscriptBox["z", "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]], "+", RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["5985", "-", RowBox[List["2944", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]], ")"]]]], "-", RowBox[List["4096", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]], ")"]]]], "-", RowBox[List["384", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "35"]], "+", RowBox[List["31", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]], ")"]]]], "-", RowBox[List["48", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["232", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]], ")"]]]]]], ")"]]]], ")"]]]]]]]] | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 | | 
   <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>  <mn> 4 </mn>  <mo> , </mo>  <mfrac>  <mn> 43 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mn> 6 </mn>  <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["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["43", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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> 39501 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 27 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 256 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 384 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 5985 </mn>  <mo> - </mo>  <mrow>  <mn> 2944 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 48 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 232 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mn> 315 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 384 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 31 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  </mrow>  <mo> - </mo>  <mn> 35 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mrow>  <mn> 4096 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  <mo> - </mo>  <mn> 1 </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>  <cn type='integer'> 4 </cn>  <cn type='rational'> 43 <sep /> 8 </cn>  </list>  <list>  <cn type='integer'> 6 </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'> 39501 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 27 <sep /> 8 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 256 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 384 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 3 <sep /> 8 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <cn type='integer'> 5985 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2944 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 3 <sep /> 8 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 48 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 232 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 3 <sep /> 8 </cn>  </apply>  </apply>  <cn type='integer'> -315 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 384 </cn>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 31 </cn>  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 3 <sep /> 8 </cn>  </apply>  </apply>  <cn type='integer'> -35 </cn>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 4096 </cn>  <apply>  <plus />  <apply>  <power />  <apply>  <plus />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='rational'> 3 <sep /> 8 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List["4", ",", FractionBox["43", "8"], ",", "6", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["256", " ", RowBox[List["(", RowBox[List[RowBox[List["384", " ", SuperscriptBox["z", "4"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]], "+", RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List["5985", "-", RowBox[List["2944", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]], ")"]]]], "-", RowBox[List["4096", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]], ")"]]]], "-", RowBox[List["384", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "35"]], "+", RowBox[List["31", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]], ")"]]]], "-", RowBox[List["48", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "315"]], "+", RowBox[List["232", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["3", "/", "8"]]]]]]], ")"]]]]]], ")"]]]], RowBox[List["39501", " ", SuperscriptBox["z", "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["27", "/", "8"]]]]]]]]]] | 
 |  
 |   
 |  
 |  
 | |   
 |  
 |  
 |  
 |  
 |  
 |  
 | | 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] |  |  | 
 | 
 
 | 
 |