| |  
 |  | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | http://functions.wolfram.com/07.23.03.cdyy.01 | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Hypergeometric2F1[45/8, 45/8, -(43/8), z] == (1/(239322993 (1 - z)^(133/8))) 
  (239322993 - 5387550168 z + 61572001920 z^2 - 492576015360 z^3 + 
   3318406840320 z^4 - 23651190571008 z^5 + 378419049136128 z^6 + 
   2162394566492160 z^7 + 2661408697221120 z^8 + 1013869979893760 z^9 + 
   111875308126208 z^10 + 2199023255552 z^11) | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["45", "8"], ",", FractionBox["45", "8"], ",", RowBox[List["-", FractionBox["43", "8"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["239322993", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["133", "/", "8"]]]]]], RowBox[List["(", RowBox[List["239322993", "-", RowBox[List["5387550168", " ", "z"]], "+", RowBox[List["61572001920", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["492576015360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3318406840320", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["23651190571008", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["378419049136128", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["2162394566492160", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["2661408697221120", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["1013869979893760", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["111875308126208", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["2199023255552", " ", SuperscriptBox["z", "11"]]]]], ")"]]]]]]]] | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 | | 
   <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>  <mfrac>  <mn> 45 </mn>  <mn> 8 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 45 </mn>  <mn> 8 </mn>  </mfrac>  </mrow>  <mo> ; </mo>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 43 </mn>  <mn> 8 </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[FractionBox["45", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["45", "8"], 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["43", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["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> 239322993 </mn>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 133 </mn>  <mo> / </mo>  <mn> 8 </mn>  </mrow>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2199023255552 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 11 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 111875308126208 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 10 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 1013869979893760 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 9 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2661408697221120 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 8 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 2162394566492160 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 7 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 378419049136128 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 6 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 23651190571008 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 5 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 3318406840320 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 492576015360 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mn> 61572001920 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mn> 5387550168 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 239322993 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='rational'> 45 <sep /> 8 </cn>  <cn type='rational'> 45 <sep /> 8 </cn>  </list>  <list>  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 43 <sep /> 8 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 239322993 </cn>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='rational'> 133 <sep /> 8 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2199023255552 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 11 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 111875308126208 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 10 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 1013869979893760 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 9 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2661408697221120 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 8 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2162394566492160 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 7 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 378419049136128 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 6 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 23651190571008 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 5 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 3318406840320 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 492576015360 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 61572001920 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 5387550168 </cn>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 239322993 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["45", "8"], ",", FractionBox["45", "8"], ",", RowBox[List["-", FractionBox["43", "8"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["239322993", "-", RowBox[List["5387550168", " ", "z"]], "+", RowBox[List["61572001920", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["492576015360", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["3318406840320", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["23651190571008", " ", SuperscriptBox["z", "5"]]], "+", RowBox[List["378419049136128", " ", SuperscriptBox["z", "6"]]], "+", RowBox[List["2162394566492160", " ", SuperscriptBox["z", "7"]]], "+", RowBox[List["2661408697221120", " ", SuperscriptBox["z", "8"]]], "+", RowBox[List["1013869979893760", " ", SuperscriptBox["z", "9"]]], "+", RowBox[List["111875308126208", " ", SuperscriptBox["z", "10"]]], "+", RowBox[List["2199023255552", " ", SuperscriptBox["z", "11"]]]]], RowBox[List["239322993", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["133", "/", "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] |  |  | 
 | 
 
 | 
 |