| |  
 |  | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | http://functions.wolfram.com/07.31.03.0134.01 | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | HypergeometricPFQ[{1, 1, c}, {2, 2, c + 1}, z] == 
 (c/((-1 + c)^2 z)) (1 - (-z)^(1 - c) (Gamma[c] - Gamma[c, -z]) - E^z - 
   (-1 + c) (EulerGamma + Gamma[0, -z] + Log[-z])) | 
 |  
 |  
 |  
 |  
 |  
 |  |   
 |  
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  
 |  
 |  
 |  
 |  
 |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "c"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", RowBox[List["c", "+", "1"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["c", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "c"]], ")"]], "2"], "z"]]], RowBox[List["(", " ", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["1", "-", "c"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], "-", " ", RowBox[List["Gamma", "[", RowBox[List["c", ",", RowBox[List["-", "z"]]]], "]"]]]], ")"]]]], "-", SuperscriptBox["\[ExponentialE]", "z"], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["EulerGamma", "+", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["-", "z"]]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List["-", "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> 3 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 3 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 1 </mn>  <mo> , </mo>  <mi> c </mi>  </mrow>  <mo> ; </mo>  <mrow>  <mn> 2 </mn>  <mo> , </mo>  <mn> 2 </mn>  <mo> , </mo>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["c", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mi> c </mi>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> c </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> c </mi>  <mo> ) </mo>  </mrow>  <mo> - </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mn> 0 </mn>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <semantics>  <mi> ℽ </mi>  <annotation encoding='Mathematica'> TagBox["\[DoubledGamma]", Function[EulerGamma]] </annotation>  </semantics>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <msup>  <mi> ⅇ </mi>  <mi> z </mi>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <cn type='integer'> 1 </cn>  <cn type='integer'> 1 </cn>  <ci> c </ci>  </list>  <list>  <cn type='integer'> 2 </cn>  <cn type='integer'> 2 </cn>  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <apply>  <times />  <ci> c </ci>  <apply>  <power />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> -1 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <ci> Gamma </ci>  <ci> c </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> Gamma </ci>  <ci> c </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <plus />  <apply>  <ci> Gamma </ci>  <cn type='integer'> 0 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <ln />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <eulergamma />  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <exponentiale />  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   | 
 |  
 |  
 |  
 |  
 |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 |  |  
 |  |  
 |  
 |  
 |  |  
 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "c_"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", RowBox[List["c_", "+", "1"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["1", "-", "c"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["c", ",", RowBox[List["-", "z"]]]], "]"]]]], ")"]]]], "-", SuperscriptBox["\[ExponentialE]", "z"], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["EulerGamma", "+", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["-", "z"]]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List["-", "z"]], "]"]]]], ")"]]]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "c"]], ")"]], "2"], " ", "z"]]]]]]] | 
 |  
 |   
 |  
 |  
 | |   
 |  
 |  
 |  
 |  
 |  
 |  
 | | 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},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] |  |  | 
 | 
 
 | 
 |