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 HypergeometricPFQ

 http://functions.wolfram.com/07.28.10.0002.01

 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 + ContinueFraction[{-(((Subscript[a, 1] + k) (Subscript[a, 2] + k) (Subscript[a, 3] + k) (Subscript[a, 4] + k) z)/ ((k + 1) (Subscript[b, 1] + k) (Subscript[b, 2] + k) (Subscript[b, 3] + k))), 1 + ((Subscript[a, 1] + k) (Subscript[a, 2] + k) (Subscript[a, 3] + k) (Subscript[a, 4] + k) z)/((k + 1) (Subscript[b, 1] + k) (Subscript[b, 2] + k) (Subscript[b, 3] + k))}, {k, 1, Infinity}])

 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["ContinueFraction", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["a", "3"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["a", "4"], "+", "k"]], ")"]], "z"]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "3"], "+", "k"]], ")"]]]]]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["a", "3"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["a", "4"], "+", "k"]], ")"]], "z"]], RowBox[List[RowBox[List["(", RowBox[List["k", "+", "1"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "1"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "2"], "+", "k"]], ")"]], RowBox[List["(", RowBox[List[SubscriptBox["b", "3"], "+", "k"]], ")"]]]]]]]]], "}"]], ",", RowBox[List["{", RowBox[List["k", ",", "1", ",", "\[Infinity]"]], "}"]]]], "]"]]]], ")"]]]]]]]]]]

 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 + Κ k ( - ( k + a 1 ) ( k + a 2 ) ( k + a 3 ) ( k + a 4 ) z ( k + 1 ) ( k + b 1 ) ( k + b 2 ) ( k + b 3 ) , 1 + ( k + a 1 ) ( k + a 2 ) ( k + a 3 ) ( k + a 4 ) z ( k + 1 ) ( k + b 1 ) ( k + b 2 ) ( k + b 3 ) ) 1 ) 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 Subscript Subscript Κ k -1 k Subscript a 1 k Subscript a 2 k Subscript a 3 k Subscript a 4 z k 1 k Subscript b 1 k Subscript b 2 k Subscript b 3 -1 1 k Subscript a 1 k Subscript a 2 k Subscript a 3 k Subscript a 4 z k 1 k Subscript b 1 k Subscript b 2 k Subscript b 3 -1 1 -1 [/itex]

 Rule Form

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

 2001-10-29