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   http://functions.wolfram.com/07.26.17.0013.01
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    Subscript[b, 2] Subscript[b, 3] c (c + 1) 
   (HypergeometricPFQ[{a, Subscript[a, 2]}, {c, Subscript[b, 2], 
      Subscript[b, 3]}, z] - HypergeometricPFQ[{a + 1, Subscript[a, 2]}, 
     {c + 1, Subscript[b, 2], Subscript[b, 3]}, z]) + 
  Subscript[a, 2] z (c - a) HypergeometricPFQ[{a + 1, Subscript[a, 2] + 1}, 
    {c + 2, Subscript[b, 2] + 1, Subscript[b, 3] + 1}, z] == 0 
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   Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["b", "2"], SubscriptBox["b", "3"], "c", RowBox[List["(", RowBox[List["c", "+", "1"]], ")"]], RowBox[List["(", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a", ",", SubscriptBox["a", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["c", ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", "z"]], "]"]], "-", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", SubscriptBox["a", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["c", "+", "1"]], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", "z"]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["a", "2"], "z", RowBox[List["(", RowBox[List["c", " ", "-", "a"]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", RowBox[List[SubscriptBox["a", "2"], "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["c", "+", "2"]], ",", RowBox[List[SubscriptBox["b", "2"], "+", "1"]], ",", RowBox[List[SubscriptBox["b", "3"], "+", "1"]]]], "}"]], ",", "z"]], "]"]]]]]], "\[Equal]", "0"]]]] 
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</mo>  <mrow>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> , </mo>  <msub>  <mi> b </mi>  <mn> 2 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> b </mi>  <mn> 3 </mn>  </msub>  </mrow>  <mo> ; </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["a", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["c", "+", "1"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "3"], 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>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msub>  <mi> b </mi>  <mn> 2 </mn>  </msub>  <mo> ⁢ </mo>  <msub>  <mi> b </mi>  <mn> 3 </mn>  </msub>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mn> 0 </mn>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  <ci> z </ci>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <plus />  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </list>  <list>  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <plus />  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 3 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> 1 </cn>  </apply>  <ci> c </ci>  <apply>  <plus />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <ci> a </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </list>  <list>  <ci> c </ci>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 3 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <plus />  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </list>  <list>  <apply>  <plus />  <ci> c </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 3 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 0 </cn>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SubscriptBox["b_", "2"], " ", SubscriptBox["b_", "3"], " ", "c_", " ", RowBox[List["(", RowBox[List["c_", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", SubscriptBox["a_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["c_", ",", SubscriptBox["b_", "2"], ",", SubscriptBox["b_", "3"]]], "}"]], ",", "z_"]], "]"]], "-", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a_", "+", "1"]], ",", SubscriptBox["a_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["c_", "+", "1"]], ",", SubscriptBox["b_", "2"], ",", SubscriptBox["b_", "3"]]], "}"]], ",", "z_"]], "]"]]]], ")"]]]], "+", RowBox[List[SubscriptBox["a_", "2"], " ", "z_", " ", RowBox[List["(", RowBox[List["c_", "-", "a_"]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a_", "+", "1"]], ",", RowBox[List[SubscriptBox["a_", "2"], "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["c_", "+", "2"]], ",", RowBox[List[SubscriptBox["b_", "2"], "+", "1"]], ",", RowBox[List[SubscriptBox["b_", "3"], "+", "1"]]]], "}"]], ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]  |  
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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,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] |  |   |  
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