html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.22.10.0001.01

 Input Form

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

 Standard Form

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

 MathML Form

 1 F 2 ( a 1 ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[SubscriptBox["a", "1"], 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]]]], 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 z b 1 b 2 / ( 1 + - z ( 1 + a 1 ) 2 ( 1 + b 1 ) ( 1 + b 2 ) / ( 1 + z ( 1 + a 1 ) 2 ( 1 + b 1 ) ( 1 + b 2 ) + - z ( 2 + a 1 ) 3 ( 2 + b 1 ) ( 2 + b 2 ) 1 + z ( 2 + a 1 ) 3 ( 2 + b 1 ) ( 2 + b 2 ) + - z ( 3 + a 1 ) 4 ( 3 + b 1 ) ( 3 + b 2 ) 1 + z ( 3 + a 1 ) 4 ( 3 + b 1 ) ( 3 + b 2 ) + ) ) HypergeometricPFQ Subscript a 1 Subscript b 1 Subscript b 2 z 1 Subscript a 1 z Subscript b 1 Subscript b 2 -1 1 -1 z 1 Subscript a 1 2 1 Subscript b 1 1 Subscript b 2 -1 1 z 1 Subscript a 1 2 1 Subscript b 1 1 Subscript b 2 -1 -1 z 2 Subscript a 1 3 2 Subscript b 1 2 Subscript b 2 -1 1 z 2 Subscript a 1 3 2 Subscript b 1 2 Subscript b 2 -1 -1 z 3 Subscript a 1 4 3 Subscript b 1 3 Subscript b 2 -1 1 z 3 Subscript a 1 4 3 Subscript b 1 3 Subscript b 2 -1 -1 -1 -1 -1 [/itex]

 Rule Form

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

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

 2001-10-29