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http://functions.wolfram.com/07.32.04.0002.01
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DomainAndRange[Function[{{Subscript[a, 1], \[Ellipsis], Subscript[a, p]},
{Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z},
HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis],
Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]},
z]]] == PowerProduct[PowerSet[Complexes, p], PowerSet[Complexes, q],
Complexes] \[LongRightArrow] Complexes
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Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "}"]], ",", " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "z"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List[RowBox[List["PowerSet", "[", RowBox[List["Complexes", ",", "p"]], "]"]], ",", RowBox[List["PowerSet", "[", RowBox[List["Complexes", ",", "q"]], "]"]], ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]
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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> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> * </mo> <mo> … </mo> <mo> * </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> } </mo> </mrow> <mo> ⋆ </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> ⋆ </mo> <mrow> <mo> … </mo> <mo> * </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> </mrow> <mo> } </mo> </mrow> <mo> * </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> a </mi> <mi> p </mi> </msub> </mrow> <mo> ; </mo> <mrow> <msub> <mi> b </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <msub> <mi> b </mi> <mi> q </mi> </msub> </mrow> <mo> ; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] </annotation> </semantics> </mrow> <mo> ∷ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mo> … </mo> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> } </mo> </mrow> <mo> ⊗ </mo> <mrow> <mo> { </mo> <mrow> <mi> ℂ </mi> <mo> ⊗ </mo> <mo> … </mo> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> } </mo> </mrow> <mo> ⊗ </mo> <mi> ℂ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <mi> ℂ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <list> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> … </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> p </ci> </apply> </apply> </list> <apply> <times /> <list> <apply> <ci> Star </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <ci> … </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> q </ci> </apply> </apply> </apply> </list> <ci> z </ci> </apply> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> … </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> p </ci> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> … </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> q </ci> </apply> </list> <ci> z </ci> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <list> <apply> <ci> CircleTimes </ci> <ci> ℂ </ci> <ci> … </ci> <ci> ℂ </ci> </apply> </list> <list> <apply> <ci> CircleTimes </ci> <ci> ℂ </ci> <ci> … </ci> <ci> ℂ </ci> </apply> </list> <ci> ℂ </ci> </apply> <ci> ℂ </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "}"]], ",", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]], ",", "z_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List[RowBox[List["PowerSet", "[", RowBox[List["Complexes", ",", "p"]], "]"]], ",", RowBox[List["PowerSet", "[", RowBox[List["Complexes", ",", "q"]], "]"]], ",", "Complexes"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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