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 HypergeometricPFQ

 http://functions.wolfram.com/07.28.06.0001.01

 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])/(Subscript[b, 1] Subscript[b, 2] Subscript[b, 3])) z + ((Subscript[a, 1] (1 + Subscript[a, 1]) Subscript[a, 2] (1 + Subscript[a, 2]) Subscript[a, 3] (1 + Subscript[a, 3]) Subscript[a, 4] (1 + Subscript[a, 4]))/(2 Subscript[b, 1] (1 + Subscript[b, 1]) Subscript[b, 2] (1 + Subscript[b, 2]) Subscript[b, 3] (1 + Subscript[b, 3]))) z^2 + \[Ellipsis] /; Abs[z] < 1

 Standard Form

 Cell[BoxData[RowBox[List[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"]]], RowBox[List[SubscriptBox["b", "1"], " ", SubscriptBox["b", "2"], " ", SubscriptBox["b", "3"]]]], "z"]], "+", RowBox[List[FractionBox[RowBox[List[SubscriptBox["a", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "1"]]], ")"]], " ", SubscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "2"]]], ")"]], " ", SubscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "3"]]], ")"]], " ", SubscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["a", "4"]]], ")"]]]], RowBox[List["2", " ", SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "1"]]], ")"]], " ", SubscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]], " ", SubscriptBox["b", "3"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "3"]]], ")"]]]]], SuperscriptBox["z", "2"]]], " ", "+", "\[Ellipsis]"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]

 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 b 1 b 2 b 3 z + a 1 ( 1 + a 1 ) a 2 ( 1 + a 2 ) a 3 ( 1 + a 3 ) a 4 ( 1 + a 4 ) 2 b 1 ( 1 + b 1 ) b 2 ( 1 + b 2 ) b 3 ( 1 + b 3 ) z 2 + /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 Condition 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 Subscript b 1 Subscript b 2 Subscript b 3 -1 z Subscript a 1 1 Subscript a 1 Subscript a 2 1 Subscript a 2 Subscript a 3 1 Subscript a 3 Subscript a 4 1 Subscript a 4 2 Subscript b 1 1 Subscript b 1 Subscript b 2 1 Subscript b 2 Subscript b 3 1 Subscript b 3 -1 z 2 z 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[RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["aa", "1"], " ", SubscriptBox["aa", "2"], " ", SubscriptBox["aa", "3"], " ", SubscriptBox["aa", "4"]]], ")"]], " ", "z"]], RowBox[List[SubscriptBox["bb", "1"], " ", SubscriptBox["bb", "2"], " ", SubscriptBox["bb", "3"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["aa", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "1"]]], ")"]], " ", SubscriptBox["aa", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "2"]]], ")"]], " ", SubscriptBox["aa", "3"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "3"]]], ")"]], " ", SubscriptBox["aa", "4"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["aa", "4"]]], ")"]]]], ")"]], " ", SuperscriptBox["z", "2"]]], RowBox[List["2", " ", SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "1"]]], ")"]], " ", SubscriptBox["bb", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", SubscriptBox["bb", "3"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "3"]]], ")"]]]]], "+", "\[Ellipsis]"]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]

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

 2001-10-29