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   http://functions.wolfram.com/07.27.03.0145.01
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    HypergeometricPFQ[{1, m, n}, {m + 1, n + 1}, z] == 
  ((m n)/((n - m) z^n)) ((1 - z^(n - m)) Log[1 - z] + 
    Sum[z^k/k, {k, 1, n - 1}] - z^(n - m) Sum[z^k/k, {k, 1, m - 1}]) /; 
 Element[m, Integers] && m > 0 && Element[n, Integers] && n > 0 
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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> 1 </mn>  <mo> , </mo>  <mi> m </mi>  <mo> , </mo>  <mi> n </mi>  </mrow>  <mo> ; </mo>  <mrow>  <mrow>  <mi> m </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <mrow>  <mi> n </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["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["m", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["n", HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["m", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["n", "+", "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>  <mrow>  <mi> m </mi>  <mo> ⁢ </mo>  <mi> n </mi>  </mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mi> m </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mi> n </mi>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <msup>  <mi> z </mi>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mi> m </mi>  </mrow>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> log </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <msup>  <mi> z </mi>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mi> m </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <mi> m </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </munderover>  <mfrac>  <msup>  <mi> z </mi>  <mi> k </mi>  </msup>  <mi> k </mi>  </mfrac>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> k </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <mi> n </mi>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </munderover>  <mfrac>  <msup>  <mi> z </mi>  <mi> k </mi>  </msup>  <mi> k </mi>  </mfrac>  </mrow>  </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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