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   http://functions.wolfram.com/07.25.10.0002.01
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    HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, 
  {Subscript[b, 1], Subscript[b, 2]}, z] == 
 1 + (Subscript[a, 1] Subscript[a, 2] z)/(Subscript[b, 1] Subscript[b, 2])/
   (1 + ContinueFraction[{-(((Subscript[a, 1] + k) (Subscript[a, 2] + k) z)/
        ((k + 1) (Subscript[b, 1] + k) (Subscript[b, 2] + k))), 
      1 + ((Subscript[a, 1] + k) (Subscript[a, 2] + k) z)/
        ((k + 1) (Subscript[b, 1] + k) (Subscript[b, 2] + k))}, 
     {k, 1, Infinity}]) 
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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>  <semantics>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> a </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ; </mo>  <mrow>  <msub>  <mi> b </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> b </mi>  <mn> 2 </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["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["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[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], 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>  <mn> 1 </mn>  <mo> + </mo>  <mfrac>  <mrow>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  <mo> ⁢ </mo>  <msub>  <mi> a </mi>  <mn> 2 </mn>  </msub>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mrow>  <msub>  <mi> b </mi>  <mn> 1 </mn>  </msub>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> b </mi>  <mn> 2 </mn>  </msub>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> + </mo>  <msubsup>  <mrow>  <msub>  <mi> Κ </mi>  <mi> k </mi>  </msub>  <mo> ( </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> a </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> b </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> b </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  <mo> , </mo>  <mrow>  <mn> 1 </mn>  <mo> + </mo>  <mfrac>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> a </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> b </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> k </mi>  <mo> + </mo>  <msub>  <mi> b </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 1 </mn>  <mi> ∞ </mi>  </msubsup>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> HypergeometricPFQ </ci>  <list>  <apply>  <ci> Subscript </ci>  <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>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  </list>  <ci> z </ci>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  <ci> z </ci>  <apply>  <power />  <apply>  <times />  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <ci> Subscript </ci>  <apply>  <apply>  <ci> Subscript </ci>  <ci> Κ </ci>  <ci> k </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <ci> z </ci>  <apply>  <power />  <apply>  <times />  <apply>  <plus />  <ci> k </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <ci> z </ci>  <apply>  <power />  <apply>  <times />  <apply>  <plus />  <ci> k </ci>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <plus />  <ci> k </ci>  <apply>  <ci> Subscript </ci>  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <infinity />  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox[RowBox[List[SubscriptBox["aa", "1"], " ", SubscriptBox["aa", "2"], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["ContinueFraction", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["aa", "1"], "+", "k"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["aa", "2"], "+", "k"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "+", "k"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "2"], "+", "k"]], ")"]]]]]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["aa", "1"], "+", "k"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["aa", "2"], "+", "k"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], "+", "k"]], ")"]], " ", RowBox[List["(", RowBox[List[SubscriptBox["bb", "2"], "+", "k"]], ")"]]]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "1", ",", "\[Infinity]"]], "}"]]]], "]"]]]], ")"]]]]]]]]]]]  |  
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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,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] |  | HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] |  |   |  
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