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 HypergeometricPFQ

 http://functions.wolfram.com/07.28.10.0001.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == 1 + (Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] Subscript[a, 4] z)/(Subscript[b, 1] Subscript[b, 2] Subscript[b, 3])/ (1 + -((z (1 + Subscript[a, 1]) (1 + Subscript[a, 2]) (1 + Subscript[a, 3]) (1 + Subscript[a, 4]))/(2 (1 + Subscript[b, 1]) (1 + Subscript[b, 2]) (1 + Subscript[b, 3])))/ (1 + (z (1 + Subscript[a, 1]) (1 + Subscript[a, 2]) (1 + Subscript[a, 3]) (1 + Subscript[a, 4]))/(2 (1 + Subscript[b, 1]) (1 + Subscript[b, 2]) (1 + Subscript[b, 3])) - (z (2 + Subscript[a, 1]) (2 + Subscript[a, 2]) (2 + Subscript[a, 3]) (2 + Subscript[a, 4]))/(3 (2 + Subscript[b, 1]) (2 + Subscript[b, 2]) (2 + Subscript[b, 3]))/ (1 + (z (2 + Subscript[a, 1]) (2 + Subscript[a, 2]) (2 + Subscript[a, 3]) (2 + Subscript[a, 4]))/ (3 (2 + Subscript[b, 1]) (2 + Subscript[b, 2]) (2 + Subscript[b, 3])) + \[Ellipsis])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"], ",", SubscriptBox["a", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"], ",", SubscriptBox["b", "3"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["1", "+", RowBox[List[FractionBox[RowBox[List[SubscriptBox["a", "1"], " ", SubscriptBox["a", "2"], SubscriptBox["a", "3"], SubscriptBox["a", "4"], "z"]], RowBox[List[" ", RowBox[List[SubscriptBox["b", "1"], SubscriptBox["b", "2"], SubscriptBox["b", "3"]]]]]], "/", RowBox[List["(", RowBox[List["1", "+", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "4"]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "3"]]], ")"]]]]]]], "/", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "4"]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "3"]]], ")"]]]]], "+", FractionBox[RowBox[List["-", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "4"]]], ")"]]]], RowBox[List["3", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "3"]]], ")"]]]]]]], RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["a", "4"]]], ")"]]]], RowBox[List["3", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["b", "3"]]], ")"]]]]], "+", "\[Ellipsis]"]]]]], ")"]]]]]], ")"]]]]]]]]]]

 MathML Form

 4 F 3 ( a 1 , a 2 , a 3 , a 4 ; b 1 , b 2 , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] 1 + ( a 1 a 2 a 3 a 4 z / ( b 1 b 2 b 3 ) ) / ( 1 + - z ( 1 + a 1 ) ( 1 + a 2 ) ( 1 + a 3 ) ( 1 + a 4 ) 2 ( 1 + b 1 ) ( 1 + b 2 ) ( 1 + b 3 ) / ( 1 + z ( 1 + a 1 ) ( 1 + a 2 ) ( 1 + a 3 ) ( 1 + a 4 ) 2 ( 1 + b 1 ) ( 1 + b 2 ) ( 1 + b 3 ) + - z ( 2 + a 1 ) ( 2 + a 2 ) ( 2 + a 3 ) ( 2 + a 4 ) 3 ( 2 + b 1 ) ( 2 + b 2 ) ( 2 + b 3 ) 1 + z ( 2 + a 1 ) ( 2 + a 2 ) ( 2 + a 3 ) ( 2 + a 4 ) 3 ( 2 + b 1 ) ( 2 + b 2 ) ( 2 + b 3 ) + ) ) HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 Subscript a 4 Subscript b 1 Subscript b 2 Subscript b 3 z 1 Subscript a 1 Subscript a 2 Subscript a 3 Subscript a 4 z Subscript b 1 Subscript b 2 Subscript b 3 -1 1 -1 z 1 Subscript a 1 1 Subscript a 2 1 Subscript a 3 1 Subscript a 4 2 1 Subscript b 1 1 Subscript b 2 1 Subscript b 3 -1 1 z 1 Subscript a 1 1 Subscript a 2 1 Subscript a 3 1 Subscript a 4 2 1 Subscript b 1 1 Subscript b 2 1 Subscript b 3 -1 -1 z 2 Subscript a 1 2 Subscript a 2 2 Subscript a 3 2 Subscript a 4 3 2 Subscript b 1 2 Subscript b 2 2 Subscript b 3 -1 1 z 2 Subscript a 1 2 Subscript a 2 2 Subscript a 3 2 Subscript a 4 3 2 Subscript b 1 2 Subscript b 2 2 Subscript b 3 -1 -1 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"], ",", SubscriptBox["a_", "3"], ",", SubscriptBox["a_", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", SubscriptBox["b_", "3"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox[RowBox[List[SubscriptBox["aa", "1"], " ", SubscriptBox["aa", "2"], " ", SubscriptBox["aa", "3"], " ", SubscriptBox["aa", "4"], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"], " ", SubscriptBox["bb", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "4"]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "3"]]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "4"]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "3"]]], ")"]]]]], "-", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "4"]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["3", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["bb", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["bb", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["bb", "3"]]], ")"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "3"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["aa", "4"]]], ")"]]]], RowBox[List["3", " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["bb", "1"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["bb", "2"]]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", SubscriptBox["bb", "3"]]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]]]]], ")"]]]]]]], ")"]]]]]]]]]]]

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

 2001-10-29