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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/07.27.04.0012.01









  


  








Input Form





BranchPoints[HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z], z] == {1, ComplexInfinity} /; NonTerminatingHypergeometricSeriesQ[ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List["1", ",", "ComplexInfinity"]], "}"]]]], "/;", RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], "]"]]]]]]








MathML Form







<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> &#8492;&#119979; </mi> <mi> z </mi> </msub> <mo> ( </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 3 </mn> </msub> <msub> <mi> F </mi> <mn> 2 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 3 </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[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;3&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;2&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;a&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;a&quot;, &quot;3&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[SubscriptBox[&quot;b&quot;, &quot;1&quot;], HypergeometricPFQ, Rule[Editable, True]], &quot;,&quot;, TagBox[SubscriptBox[&quot;b&quot;, &quot;2&quot;], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, HypergeometricPFQ, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]] </annotation> </semantics> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#119977;&#119983; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> { </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8492;&#119979; </ci> <ci> z </ci> </apply> <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> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </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> <list> <cn type='integer'> 1 </cn> <apply> <ci> OverTilde </ci> <infinity /> </apply> </list> </apply> <apply> <ci> &#119977;&#119983; </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> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"], ",", SubscriptBox["a_", "3"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "ComplexInfinity"]], "}"]], "/;", RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], "]"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29