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AppellF1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > AppellF1[a,b1,b2,c,z1,z2] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/07.36.04.0003.01









  


  








Input Form





AppellF1[Conjugate[a], Conjugate[Subscript[b, 1]], Conjugate[Subscript[b, 2]], Conjugate[c], Conjugate[Subscript[z, 1]], Conjugate[Subscript[z, 2]]] == Conjugate[AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[z, 1], Subscript[z, 2]]] /; !IntervalMemberQ[Interval[{1, Infinity}], Subscript[z, 1]] && !IntervalMemberQ[Interval[{1, Infinity}], Subscript[z, 2]]








Standard Form





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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> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mrow> <mover> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <mi> c </mi> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mover> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mrow> <mover> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <mi> c </mi> <mo> _ </mo> </mover> <mo> ; </mo> <mover> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> , </mo> <mover> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <mrow> <semantics> <msub> <mi> F </mi> <mn> 1 </mn> </msub> <annotation-xml encoding='MathML-Content'> <ci> AppellF1 </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ; </mo> <msub> <mi> b </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> _ </mo> </mover> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29