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 | | http://functions.wolfram.com/07.25.04.0005.01 | 
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 | | Singularities[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, 
    {Subscript[b, 1], Subscript[b, 2]}, z], z] == 
  {{ComplexInfinity, Infinity}} /; 
  !((Element[-Subscript[a, 1], Integers] && -Subscript[a, 1] >= 0) || 
   (Element[-Subscript[a, 2], Integers] && -Subscript[a, 2] >= 0)) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Singularities", "[", RowBox[List[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"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]]]], "/;", RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "\[GreaterEqual]", "0"]]]], "\[Or]", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], ",", "Integers"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "\[GreaterEqual]", "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>  <msub>  <mi> 𝒮𝒾𝓃ℊ </mi>  <mi> z </mi>  </msub>  <mo> ( </mo>  <mrow>  <mrow>  <msub>  <mo>   </mo>  <mn> 2 </mn>  </msub>  <msub>  <mi> F </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <semantics>  <mrow>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> a </mi>  <mn> 2 </mn>  </msub>  </mrow>  <annotation encoding='Mathematica'> 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]] </annotation>  </semantics>  <mo> ; </mo>  <semantics>  <mrow>  <msub>  <mi> b </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> b </mi>  <mn> 2 </mn>  </msub>  </mrow>  <annotation encoding='Mathematica'> 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]] </annotation>  </semantics>  <mo> ; </mo>  <semantics>  <mi> z </mi>  <annotation encoding='Mathematica'> TagBox["z", HypergeometricPFQ, Rule[Editable, True]] </annotation>  </semantics>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mo> { </mo>  <mrow>  <mo> { </mo>  <mrow>  <mover>  <mi> ∞ </mi>  <mo> ~ </mo>  </mover>  <mo> , </mo>  <mi> ∞ </mi>  </mrow>  <mo> } </mo>  </mrow>  <mo> } </mo>  </mrow>  </mrow>  <mo> /; </mo>  <mrow>  <mo> ¬ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <msub>  <mi> a </mi>  <mn> 1 </mn>  </msub>  </mrow>  <mo> ∈ </mo>  <mi> ℕ </mi>  </mrow>  <mo> ∨ </mo>  <mrow>  <mrow>  <mo> - </mo>  <msub>  <mi> a </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ∈ </mo>  <mi> ℕ </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> FormBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <ms> 𝒮𝒾𝓃ℊ </ms>  <ms> z </ms>  </apply>  <ms> [ </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> SubscriptBox </ci>  <apply>  <ci> ErrorBox </ci>  <ms>  </ms>  </apply>  <apply>  <ci> FormBox </ci>  <ms> 2 </ms>  <ci> TraditionalForm </ci>  </apply>  </apply>  <apply>  <ci> SubscriptBox </ci>  <ms> F </ms>  <apply>  <ci> FormBox </ci>  <ms> 2 </ms>  <ci> TraditionalForm </ci>  </apply>  </apply>  </list>  </apply>  <ms> ⁡ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> ( </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> 1 </ms>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> , </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> 2 </ms>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  <apply>  <ci> InterpretTemplate </ci>  <apply>  <ci> Function </ci>  <list>  <apply>  <ci> SlotSequence </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  </apply>  </apply>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <false />  </apply>  </apply>  <ms> ; </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> TagBox </ci>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> b </ms>  <ms> 1 </ms>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  <ms> , </ms>  <apply>  <ci> TagBox </ci>  <apply>  <ci> SubscriptBox </ci>  <ms> b </ms>  <ms> 2 </ms>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  <apply>  <ci> InterpretTemplate </ci>  <apply>  <ci> Function </ci>  <list>  <apply>  <ci> SlotSequence </ci>  <cn type='integer'> 1 </cn>  </apply>  </list>  </apply>  </apply>  </apply>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <false />  </apply>  </apply>  <ms> ; </ms>  <apply>  <ci> TagBox </ci>  <ms> z </ms>  <ci> HypergeometricPFQ </ci>  <apply>  <ci> Rule </ci>  <ci> Editable </ci>  <true />  </apply>  </apply>  </list>  </apply>  <ms> ) </ms>  </list>  </apply>  </list>  </apply>  <ms> ] </ms>  </list>  </apply>  <ms> ⩵ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> { </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> { </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> OverscriptBox </ci>  <ms> ∞ </ms>  <ms> ~ </ms>  </apply>  <ms> , </ms>  <ms> ∞ </ms>  </list>  </apply>  <ms> } </ms>  </list>  </apply>  <ms> } </ms>  </list>  </apply>  </list>  </apply>  <ms> /; </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> ¬ </ms>  <apply>  <ci> RowBox </ci>  <list>  <ms> ( </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <ms> - </ms>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> 1 </ms>  </apply>  </list>  </apply>  <ms> ∈ </ms>  <ms> ℕ </ms>  </list>  </apply>  <ms> ∨ </ms>  <apply>  <ci> RowBox </ci>  <list>  <apply>  <ci> RowBox </ci>  <list>  <ms> - </ms>  <apply>  <ci> SubscriptBox </ci>  <ms> a </ms>  <ms> 2 </ms>  </apply>  </list>  </apply>  <ms> ∈ </ms>  <ms> ℕ </ms>  </list>  </apply>  </list>  </apply>  <ms> ) </ms>  </list>  </apply>  </list>  </apply>  </list>  </apply>  <ci> TraditionalForm </ci>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Singularities", "[", RowBox[List[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_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["{", RowBox[List["ComplexInfinity", ",", "\[Infinity]"]], "}"]], "}"]], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "\[GreaterEqual]", "0"]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "\[GreaterEqual]", "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,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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