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; }

 KelvinBer

 http://functions.wolfram.com/03.14.26.0030.01

 Input Form

 Hypergeometric0F1[1, (I z^2)/4] KelvinBer[z] == (1/2) Sqrt[Pi/2] (Sqrt[2] Pi MeijerG[{{}, {1/2}}, {{0}, {0, 1/2, 0, 1/2}}, z^4/64] + MeijerG[{{3/4, 1/4}, {}}, {{0}, {0, 1/2, 1/2, 1/2, 0}}, z^4/16] + I MeijerG[{{3/4, 1/4}, {}}, {{1/2}, {0, 0, 1/2, 1/2, 0}}, z^4/16]) /; Inequality[-(Pi/4), Less, Arg[z], LessEqual, Pi/4] || Inequality[(3 Pi)/4, Less, Arg[z], LessEqual, Pi] || Inequality[-Pi, Less, Arg[z], LessEqual, (5 Pi)/4]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["Hypergeometric0F1", "[", RowBox[List["1", ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"]]], "]"]], " ", RowBox[List["KelvinBer", "[", "z", "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["2"], " ", "\[Pi]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", "0", ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "64"]]], "]"]]]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "0"]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "16"]]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0", ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "0"]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "16"]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "4"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "4"]]], "\[Or]", RowBox[List[FractionBox[RowBox[List["3", "\[Pi]"]], "4"], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "\[Or]", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["5", "\[Pi]"]], "4"]]]]]]]]]

 MathML Form

 0 F 1 ( ; 1 ; z 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["1", Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"], Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric0F1] ber ( z ) 1 2 π 2 ( 2 π G 1 , 5 1 , 0 ( z 4 64 1 2 0 , 0 , 1 2 , 0 , 1 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "5"]], RowBox[List["1", ",", "0"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[SuperscriptBox["z", "4"], "64"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] + G 2 , 6 1 , 2 ( z 4 16 3 4 , 1 4 0 , 0 , 1 2 , 1 2 , 1 2 , 0 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "6"]], RowBox[List["1", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[SuperscriptBox["z", "4"], "16"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox["3", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] + G 2 , 6 1 , 2 ( z 4 16 3 4 , 1 4 1 2 , 0 , 0 , 1 2 , 1 2 , 0 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "6"]], RowBox[List["1", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[SuperscriptBox["z", "4"], "16"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox["3", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) /; - π 4 < arg ( z ) π 4 3 π 4 < arg ( z ) π - π < arg ( z ) 5 π 4 Condition Hypergeometric0F1 1 z 2 4 -1 KelvinBer z 1 2 2 -1 1 2 2 1 2 MeijerG 1 2 0 0 1 2 0 1 2 z 4 64 -1 MeijerG 3 4 1 4 0 0 1 2 1 2 1 2 0 z 4 16 -1 MeijerG 3 4 1 4 1 2 0 0 1 2 1 2 0 z 4 16 -1 Inequality -1 4 -1 z 4 -1 Inequality 3 4 -1 z Inequality -1 z 5 4 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Hypergeometric0F1", "[", RowBox[List["1", ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z_", "2"]]], "4"]]], "]"]], " ", RowBox[List["KelvinBer", "[", "z_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", SqrtBox[FractionBox["\[Pi]", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["2"], " ", "\[Pi]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", "0", ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "64"]]], "]"]]]], "+", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "0"]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "16"]]], "]"]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["1", "4"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0", ",", FractionBox["1", "2"], ",", FractionBox["1", "2"], ",", "0"]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "16"]]], "]"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "4"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "4"]]], "||", RowBox[List[FractionBox[RowBox[List["3", " ", "\[Pi]"]], "4"], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "||", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["5", " ", "\[Pi]"]], "4"]]]]]]]]]]]

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

 2007-05-02