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 HypergeometricPFQ

 http://functions.wolfram.com/07.28.02.0002.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, i], \[Ellipsis], Subscript[a, 4]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, j], \[Ellipsis], Subscript[b, 3]}, z] == Sum[(Pochhammer[Subscript[a, 1], k] Pochhammer[Subscript[a, 2], k] Pochhammer[Subscript[a, 3], k] Pochhammer[Subscript[a, 4], k] z^k)/ (Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k] Pochhammer[Subscript[b, 3], k] k!), {k, 0, n}] /; Subscript[a, i] == -n && Subscript[b, j] == -m && Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0 && m >= n

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "i"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "j"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "3"]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["a", "1"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["a", "2"], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["a", "3"], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["a", "4"], ",", "k"]], "]"]], " ", SuperscriptBox["z", "k"]]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["b", "1"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["b", "2"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[SubscriptBox["b", "3"], ",", "k"]], "]"]], " ", RowBox[List["k", "!"]]]]]]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["a", "i"], "\[Equal]", RowBox[List["-", "n"]]]], "\[And]", RowBox[List[SubscriptBox["b", "j"], "\[Equal]", RowBox[List["-", "m"]]]], "\[And]", RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["m", "\[GreaterEqual]", "n"]]]]]]]]

 MathML Form

 4 F 3 ( a 1 , , a i , , a 4 ; b 1 , , b j , , b 3 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "i"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "j"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] k = 0 n ( a 1 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "1"], ")"]], "k"], Pochhammer] ( a 2 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "2"], ")"]], "k"], Pochhammer] ( a 3 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "3"], ")"]], "k"], Pochhammer] ( a 4 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "4"], ")"]], "k"], Pochhammer] z k ( b 1 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "1"], ")"]], "k"], Pochhammer] ( b 2 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "2"], ")"]], "k"], Pochhammer] ( b 3 ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "3"], ")"]], "k"], Pochhammer] k ! /; a i - n b j - m m n m n FormBox RowBox RowBox TagBox RowBox RowBox SubscriptBox FormBox 4 TraditionalForm SubscriptBox F FormBox 3 TraditionalForm RowBox ( RowBox SubscriptBox a 1 , , RowBox TagBox TagBox RowBox TagBox SubscriptBox a i HypergeometricPFQ Rule Editable , TagBox HypergeometricPFQ Rule Editable , TagBox SubscriptBox a 4 HypergeometricPFQ Rule Editable InterpretTemplate Function SlotSequence 1 HypergeometricPFQ Rule Editable ; TagBox TagBox RowBox TagBox ErrorBox RowBox SubscriptBox b 1 , , SubscriptBox b j HypergeometricPFQ Rule Editable , TagBox HypergeometricPFQ Rule Editable , TagBox SubscriptBox b 3 HypergeometricPFQ Rule Editable Function Null HoldComplete SlotSequence 1 HoldAllComplete HypergeometricPFQ Rule Editable ; TagBox z HypergeometricPFQ Rule Editable ) Function Null HoldComplete HypergeometricPFQ Slot 1 Slot 2 Slot 3 HoldAllComplete RowBox UnderoverscriptBox RowBox k = 0 n FractionBox RowBox TagBox SubscriptBox RowBox ( SubscriptBox a 1 ) k Pochhammer TagBox SubscriptBox RowBox ( SubscriptBox a 2 ) k Pochhammer TagBox SubscriptBox RowBox ( SubscriptBox a 3 ) k Pochhammer TagBox SubscriptBox RowBox ( SubscriptBox a 4 ) k Pochhammer SuperscriptBox z k RowBox TagBox SubscriptBox RowBox ( SubscriptBox b 1 ) k Pochhammer TagBox SubscriptBox RowBox ( SubscriptBox b 2 ) k Pochhammer TagBox SubscriptBox RowBox ( SubscriptBox b 3 ) k Pochhammer RowBox k ! /; RowBox RowBox SubscriptBox a i RowBox - n RowBox SubscriptBox b j RowBox - m RowBox m RowBox n RowBox m n TraditionalForm [/itex]

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

 2001-10-29