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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/07.23.04.0014.01









  


  








Input Form





RamificationIndex[Hypergeometric2F1[a, b, c, z], z, ComplexInfinity] == Log /; Element[a - b, Integers] || !(Element[a, Rationals] && Element[b, Rationals])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", "b", ",", "c", ",", "z"]], "]"]], ",", "z", ",", "ComplexInfinity"]], "]"]], "\[Equal]", "Log"]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List[RowBox[List["a", "-", "b"]], ",", "Integers"]], "]"]], "\[Or]", RowBox[List["(", RowBox[List["Not", "[", RowBox[List[RowBox[List["Element", "[", RowBox[List["a", ",", "Rationals"]], "]"]], "\[And]", RowBox[List["Element", "[", RowBox[List["b", ",", "Rationals"]], "]"]]]], "]"]], ")"]]]]]]]]








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> &#8475; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;a&quot;, Hypergeometric2F1, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;b&quot;, Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[&quot;c&quot;, Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[&quot;z&quot;, Hypergeometric2F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]] </annotation> </semantics> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mi> log </mi> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8744; </mo> <mrow> <mo> &#172; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8712; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> b </mi> <mo> &#8712; </mo> <semantics> <mi> &#8474; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalQ]&quot;, Function[Rationals]] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8475; </ci> <ci> z </ci> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <ci> a </ci> <ci> b </ci> </list> <list> <ci> c </ci> </list> <ci> z </ci> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </apply> <ci> log </ci> </apply> <apply> <or /> <apply> <in /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <integers /> </apply> <apply> <not /> <apply> <and /> <apply> <in /> <ci> a </ci> <rationals /> </apply> <apply> <in /> <ci> b </ci> <rationals /> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", "b_", ",", "c_", ",", "z_"]], "]"]], ",", "z_", ",", "ComplexInfinity"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["Log", "/;", RowBox[List[RowBox[List[RowBox[List["a", "-", "b"]], "\[Element]", "Integers"]], "||", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List["a", "\[Element]", "Rationals"]], "&&", RowBox[List["b", "\[Element]", "Rationals"]]]], ")"]]]]]]]]]]]]


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





2001-10-29