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   http://functions.wolfram.com/07.32.25.0001.01
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    Limit[HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], 
      Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, 
     z]/(1 - z)^Subscript[\[Psi], q], z -> 1] == 
  Gamma[-Subscript[\[Psi], q]]/Product[Gamma[Subscript[a, j]], 
    {j, 1, q + 1}] /; Subscript[\[Psi], q] == 
   Sum[Subscript[b, j], {j, 1, q}] - Sum[Subscript[a, j], {j, 1, q + 1}] && 
  Re[Subscript[\[Psi], q]] < 0 
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   Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["-", SubscriptBox["\[Psi]", "q"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", RowBox[List["q", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]]]], ",", RowBox[List["z", "\[Rule]", "1"]]]], "]"]], "\[Equal]", FractionBox[RowBox[List["Gamma", "[", RowBox[List["-", SubscriptBox["\[Psi]", "q"]]], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], RowBox[List["q", "+", "1"]]], RowBox[List["Gamma", "[", SubscriptBox["a", "j"], "]"]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["\[Psi]", "q"], "\[Equal]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "q"], SubscriptBox["b", "j"]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], RowBox[List["q", "+", "1"]]], SubscriptBox["a", "j"]]]]]]], "\[And]", RowBox[List[RowBox[List["Re", "[", SubscriptBox["\[Psi]", "q"], "]"]], "<", "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>  <mrow>  <munder>  <mi> lim </mi>  <mrow>  <mi> z </mi>  <semantics>  <mo> → </mo>  <annotation encoding='Mathematica'> "\[Rule]" </annotation>  </semantics>  <mn> 1 </mn>  </mrow>  </munder>  <mo> ⁢ </mo>  <mtext>   </mtext>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mo> - </mo>  <msub>  <mi> ψ </mi>  <mi> q </mi>  </msub>  </mrow>  </msup>  <mo> ⁢ </mo>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mrow>  <mi> q </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </msub>  <msub>  <mover>  <mi> F </mi>  <mo> ~ </mo>  </mover>  <mi> q </mi>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <mo> … </mo>  <mo> , </mo>  <msub>  <mi> a </mi>  <mrow>  <mi> q </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </msub>  </mrow>  <mo> ; </mo>  <mrow>  <msub>  <mi> b </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <mo> … </mo>  <mo> , </mo>  <msub>  <mi> b </mi>  <mi> q </mi>  </msub>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["q", "+", "1"]], TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", RowBox[List["q", "+", "1"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation>  </semantics>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mfrac>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mo> - </mo>  <msub>  <mi> ψ </mi>  <mi> q </mi>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <munderover>  <mo> ∏ </mo>  <mrow>  <mi> j </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <mi> q </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </munderover>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <msub>  <mi> a </mi>  <mi> j </mi>  </msub>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  <mo> /; </mo>  <mrow>  <mrow>  <msub>  <mi> ψ </mi>  <mi> q </mi>  </msub>  <mo> ⩵ </mo>  <mrow>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> j </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mi> q </mi>  </munderover>  <msub>  <mi> b </mi>  <mi> j </mi>  </msub>  </mrow>  <mo> - </mo>  <mrow>  <munderover>  <mo> ∑ </mo>  <mrow>  <mi> j </mi>  <mo> = </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <mi> q </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  </munderover>  <msub>  <mi> a </mi>  <mi> j </mi>  </msub>  </mrow>  </mrow>  </mrow>  <mo> ∧ </mo>  <mrow>  <mrow>  <mi> Re </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <msub>  <mi> ψ </mi>  <mi> q </mi>  </msub>  <mo> ) </mo>  </mrow>  <mo> < </mo>  <mn> 0 </mn>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <apply>  <limit />  <bvar>  <ci> z </ci>  </bvar>  <condition>  <apply>  <tendsto />  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  </condition>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> Subscript </ci>  <ci> ψ </ci>  <ci> q </ci>  </apply>  </apply>  </apply>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <ci> … </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <apply>  <plus />  <ci> q </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  </list>  <list>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  <ci> … </ci>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <ci> q </ci>  </apply>  </list>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <ci> Gamma </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> Subscript </ci>  <ci> ψ </ci>  <ci> q </ci>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <product />  <bvar>  <ci> j </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <apply>  <plus />  <ci> q </ci>  <cn type='integer'> 1 </cn>  </apply>  </uplimit>  <apply>  <ci> Gamma </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <ci> j </ci>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <and />  <apply>  <eq />  <apply>  <ci> Subscript </ci>  <ci> ψ </ci>  <ci> q </ci>  </apply>  <apply>  <plus />  <apply>  <sum />  <bvar>  <ci> j </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <ci> q </ci>  </uplimit>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <ci> j </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <sum />  <bvar>  <ci> j </ci>  </bvar>  <lowlimit>  <cn type='integer'> 1 </cn>  </lowlimit>  <uplimit>  <apply>  <plus />  <ci> q </ci>  <cn type='integer'> 1 </cn>  </apply>  </uplimit>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <ci> j </ci>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <lt />  <apply>  <real />  <apply>  <ci> Subscript </ci>  <ci> ψ </ci>  <ci> q </ci>  </apply>  </apply>  <cn type='integer'> 0 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Limit", "[", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z_"]], ")"]], RowBox[List["-", SubscriptBox["\[Psi]_", "q_"]]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", RowBox[List["q_", "+", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]]]], ",", RowBox[List["z_", "\[Rule]", "1"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["Gamma", "[", RowBox[List["-", SubscriptBox["\[Psi]\[Psi]", "q"]]], "]"]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "1"]], RowBox[List["q", "+", "1"]]], RowBox[List["Gamma", "[", SubscriptBox["a", "j"], "]"]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["\[Psi]\[Psi]", "q"], "\[Equal]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "q"], SubscriptBox["b", "j"]]], "-", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], RowBox[List["q", "+", "1"]]], SubscriptBox["a", "j"]]]]]]], "&&", RowBox[List[RowBox[List["Re", "[", SubscriptBox["\[Psi]\[Psi]", "q"], "]"]], "<", "0"]]]]]]]]]]  |  
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