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http://functions.wolfram.com/07.24.26.0058.01
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UnitStep[1 - Abs[z]] Hypergeometric2F1Regularized[a, b, c, -z] ==
Gamma[1 - a] Gamma[1 - b] MeijerG[{{}, {1 - a, 1 - b}}, {{0}, {1 - c}}, z]
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Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z", "]"]]]], "]"]], RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a", ",", "b", ",", "c", ",", RowBox[List["-", "z"]]]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", RowBox[List["1", "-", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "c"]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]]]]]]
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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> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> z </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ; </mo> <mi> c </mi> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["a", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox["b", Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["c", Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] </annotation> </semantics> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> a </mi> </mrow> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> c </mi> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "2"]], RowBox[List["1", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", "a"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "b"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "c"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <ci> UnitStep </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1Regularized </ci> <ci> a </ci> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list /> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </list> </list> <list> <list> <cn type='integer'> 0 </cn> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </list> </list> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["a_", ",", "b_", ",", "c_", ",", RowBox[List["-", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", RowBox[List["1", "-", "b"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "c"]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQRegularized[{},{b},z] | HypergeometricPFQRegularized[{a1},{b1},z] | HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] | |
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