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http://functions.wolfram.com/07.31.25.0005.01
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Limit[HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]},
{b, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, b z],
b -> Infinity] == HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis],
Subscript[a, p]}, {Subscript[b, 2], \[Ellipsis], Subscript[b, q]}, z]
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Cell[BoxData[RowBox[List[RowBox[List["Limit", "[", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List["b", ",", SubscriptBox["b", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", RowBox[List["b", " ", "z"]]]], "]"]], ",", RowBox[List["b", "\[Rule]", "\[Infinity]"]]]], "]"]], "\[Equal]", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]], ",", "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> <munder> <mi> lim </mi> <mrow> <mi> a </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> ; </mo> <mi> b </mi> </mrow> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> ; </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", "b"]], ",", SubscriptBox["b", "2"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", RowBox[List["b", " ", "z"]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mo> ⩵ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> ; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> ; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["q", "-", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", SubscriptBox["b", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <munder> <mi> lim </mi> <mrow> <mi> a </mi> <semantics> <mo> → </mo> <annotation encoding='Mathematica'> "\[Rule]" </annotation> </semantics> <mi> ∞ </mi> </mrow> </munder> <mo> ⁢ </mo> <mtext>   </mtext> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mi> q </mi> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> ; </mo> <mi> b </mi> </mrow> <mo> , </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> ; </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox["q", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", "b"]], ",", SubscriptBox["b", "2"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", RowBox[List["b", " ", "z"]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> <mo> ⩵ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mi> p </mi> </msub> <msub> <mi> F </mi> <mrow> <mi> q </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> a </mi> <mi> p </mi> </msub> <mo> ; </mo> <msub> <mi> b </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <mo> … </mo> <mo> , </mo> <mrow> <msub> <mi> b </mi> <mi> q </mi> </msub> <mo> ; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["p", TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["q", "-", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "p"], ";", SubscriptBox["b", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["b", "q"], ";", "z"]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] </annotation> </semantics> </mrow> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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HypergeometricPFQ[{},{},z] | HypergeometricPFQ[{},{b},z] | HypergeometricPFQ[{a},{},z] | HypergeometricPFQ[{a},{b},z] | HypergeometricPFQ[{a1},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1},z] | HypergeometricPFQ[{a1,a2},{b1,b2},z] | HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] | HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] | HypergeometricPFQ[{a1,a2,a3,a4,a5,a6},{b1,b2,b3,b4,b5},z] | |
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