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; }

 Hypergeometric0F1Regularized

 http://functions.wolfram.com/07.18.26.0154.01

 Input Form

 Hypergeometric0F1Regularized[b, z^2/4] BesselK[b, z] == 2^(-1 + b) (z^(-b) - (Pi^(3/2)/Sqrt[2]) Csc[(1/4) (1 + 4 b) Pi] MeijerG[{{(1 - b)/2, 1 - b/2}, {(3 - 2 b)/4, (1 + 2 b)/4}}, {{1 - b/2, b/2}, {(3 - 2 b)/4, 1 - (3 b)/2, -(b/2), (1 + 2 b)/4}}, z^2]) /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[" ", RowBox[List[RowBox[List[RowBox[List[RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List["b", ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]], RowBox[List["BesselK", "[", RowBox[List["b", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List["-", "b"]]], "-", RowBox[List[FractionBox[SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], SqrtBox["2"]], " ", RowBox[List["Csc", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", "\[Pi]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "b"]], "2"], ",", RowBox[List["1", "-", FractionBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", RowBox[List["2", "b"]]]], "4"], " ", ",", FractionBox[RowBox[List["1", "+", RowBox[List["2", "b"]]]], "4"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["b", "2"]]], ",", FractionBox["b", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", RowBox[List["2", "b"]]]], "4"], ",", RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "b"]], "2"]]], ",", RowBox[List["-", FractionBox["b", "2"]]], ",", FractionBox[RowBox[List["1", "+", RowBox[List["2", "b"]]]], "4"]]], " ", "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

 MathML Form

 0 F ~ 1 ( ; b ; z 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox[OverscriptBox["F", "~"], "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["b", Hypergeometric0F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1Regularized, Rule[Editable, False]], ";", TagBox[FractionBox[SuperscriptBox["z", "2"], "4"], Hypergeometric0F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric0F1Regularized] K b ( z ) 2 b - 1 ( z - b - π 3 / 2 csc ( 1 4 ( 4 b + 1 ) π ) 2 G 4 , 6 2 , 2 ( z 2 1 - b 2 , 1 - b 2 , 1 4 ( 3 - 2 b ) , 1 4 ( 2 b + 1 ) 1 - b 2 , b 2 , 1 4 ( 3 - 2 b ) , 1 - 3 b 2 , - b 2 , 1 4 ( 2 b + 1 ) ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "6"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[SuperscriptBox["z", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", "b"]], "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["b", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "b"]], "+", "1"]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["b", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["b", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "b"]], "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["b", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "b"]], "+", "1"]], ")"]]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) /; - π 2 < arg ( z ) π 2 Condition Hypergeometric0F1Regularized b z 2 4 -1 BesselK b z 2 b -1 z -1 b -1 3 2 1 4 4 b 1 2 1 2 -1 MeijerG 1 -1 b 2 -1 1 -1 b 2 -1 1 4 3 -1 2 b 1 4 2 b 1 1 -1 b 2 -1 b 2 -1 1 4 3 -1 2 b 1 -1 3 b 2 -1 -1 b 2 -1 1 4 2 b 1 z 2 Inequality -1 2 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List["b_", ",", FractionBox[SuperscriptBox["z_", "2"], "4"]]], "]"]], " ", RowBox[List["BesselK", "[", RowBox[List["b_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List["-", "b"]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Csc", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "b"]]]], ")"]], " ", "\[Pi]"]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "b"]], "2"], ",", RowBox[List["1", "-", FractionBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["b", "2"]]], ",", FractionBox["b", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], ",", RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "b"]], "2"]]], ",", RowBox[List["-", FractionBox["b", "2"]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], SqrtBox["2"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2007-05-02