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   http://functions.wolfram.com/07.27.03.0037.01
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    HypergeometricPFQ[{2, b, c}, {b + 2, c + 2}, 1] == 
  ((b (b + 1) c (c + 1) (b + c - 1))/Pochhammer[b - c - 1, 3]) 
   (PolyGamma[b] - PolyGamma[c] - (2 (b - c))/(b + c - 1)) /; 
 c != b - 1 && c != b && c != b + 1 
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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>  <mrow>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 3 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> , </mo>  <mi> b </mi>  <mo> , </mo>  <mi> c </mi>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  </mrow>  <mo> ; </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["b", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["c", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["b", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "+", "2"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["1", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <semantics>  <msub>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 3 </mn>  </msub>  <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["b", "-", "c", "-", "1"]], ")"]], "3"], Pochhammer] </annotation>  </semantics>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <semantics>  <mi> ψ </mi>  <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation>  </semantics>  <mo> ( </mo>  <mi> b </mi>  <mo> ) </mo>  </mrow>  <mo> - </mo>  <mrow>  <semantics>  <mi> ψ </mi>  <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation>  </semantics>  <mo> ( </mo>  <mi> c </mi>  <mo> ) </mo>  </mrow>  <mo> - </mo>  <mfrac>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mi> c </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> /; 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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},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2},z] |  | HypergeometricPFQ[{a1,a2},{b1,b2,b3},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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