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; }

 KelvinKer

 http://functions.wolfram.com/03.16.21.0002.01

 Input Form

 Integrate[(t^(\[Alpha] - 1) KelvinKer[t])/E^(p t), {t, 0, Infinity}] == (1/3) 2^(-3 + \[Alpha]) (2 p Gamma[(1 + \[Alpha])/2]^2 (-6 Cos[(1/4) Pi (1 + \[Alpha])] HypergeometricPFQ[ {1/4 + \[Alpha]/4, 1/4 + \[Alpha]/4, 3/4 + \[Alpha]/4, 3/4 + \[Alpha]/4}, {1/2, 3/4, 5/4}, -p^4] + p^2 (1 + \[Alpha])^2 Cos[(1/4) (Pi - Pi \[Alpha])] HypergeometricPFQ[{3/4 + \[Alpha]/4, 3/4 + \[Alpha]/4, 5/4 + \[Alpha]/4, 5/4 + \[Alpha]/4}, {5/4, 3/2, 7/4}, -p^4]) + 3 Gamma[\[Alpha]/2]^2 (2 Cos[(Pi \[Alpha])/4] HypergeometricPFQ[ {1/2 + \[Alpha]/4, 1/2 + \[Alpha]/4, \[Alpha]/4, \[Alpha]/4}, {1/4, 1/2, 3/4}, -p^4] - p^2 \[Alpha]^2 Sin[(Pi \[Alpha])/4] HypergeometricPFQ[{1/2 + \[Alpha]/4, 1/2 + \[Alpha]/4, 1 + \[Alpha]/4, 1 + \[Alpha]/4}, {3/4, 5/4, 3/2}, -p^4])) /; Re[\[Alpha]] > 0 && Re[p] > -(1/Sqrt[2])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[SuperscriptBox["t", RowBox[List["\[Alpha]", "-", "1"]]], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "p"]], " ", "t"]]], RowBox[List["KelvinKer", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "3"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "+", "\[Alpha]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "p", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "+", "\[Alpha]"]], "2"], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", "\[Alpha]"]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["p", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "\[Alpha]"]], ")"]], "2"], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["\[Pi]", " ", "\[Alpha]"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]]]], ")"]]]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["\[Alpha]", "2"], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Alpha]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", FractionBox["\[Alpha]", "4"], ",", FractionBox["\[Alpha]", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["p", "2"], " ", SuperscriptBox["\[Alpha]", "2"], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Alpha]"]], "4"], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "\[Alpha]", "]"]], ">", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "p", "]"]], ">", RowBox[List["-", FractionBox["1", SqrtBox["2"]]]]]]]]]]]]

 MathML Form

 0 t α - 1 - p t ker ( t ) t 1 3 2 α - 3 ( 3 ( 2 cos ( π α 4 ) 4 F 3 ( α 4 + 1 2 , α 4 + 1 2 , α 4 , α 4 ; 1 4 , 1 2 , 3 4 ; - p 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[Alpha]", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[Alpha]", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", SuperscriptBox["p", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - p 2 α 2 sin ( π α 4 ) 4 F 3 ( α 4 + 1 2 , α 4 + 1 2 , α 4 + 1 , α 4 + 1 ; 3 4 , 5 4 , 3 2 ; - p 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", SuperscriptBox["p", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ) Γ ( α 2 ) 2 + 2 p Γ ( α + 1 2 ) 2 ( p 2 ( α + 1 ) 2 cos ( 1 4 ( π - π α ) ) 4 F 3 ( α 4 + 3 4 , α 4 + 3 4 , α 4 + 5 4 , α 4 + 5 4 ; 5 4 , 3 2 , 7 4 ; - p 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["5", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["5", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", SuperscriptBox["p", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 6 cos ( 1 4 π ( α + 1 ) ) 4 F 3 ( α 4 + 1 4 , α 4 + 1 4 , α 4 + 3 4 , α 4 + 3 4 ; 1 2 , 3 4 , 5 4 ; - p 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Alpha]", "4"], "+", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", SuperscriptBox["p", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ) ) /; Re ( α ) > 0 Re ( p ) > - 1 2 Condition t 0 t α -1 -1 p t KelvinKer t 1 3 2 α -3 3 2 α 4 -1 HypergeometricPFQ α 4 -1 1 2 α 4 -1 1 2 α 4 -1 α 4 -1 1 4 1 2 3 4 -1 p 4 -1 p 2 α 2 α 4 -1 HypergeometricPFQ α 4 -1 1 2 α 4 -1 1 2 α 4 -1 1 α 4 -1 1 3 4 5 4 3 2 -1 p 4 Gamma α 2 -1 2 2 p Gamma α 1 2 -1 2 p 2 α 1 2 1 4 -1 α HypergeometricPFQ α 4 -1 3 4 α 4 -1 3 4 α 4 -1 5 4 α 4 -1 5 4 5 4 3 2 7 4 -1 p 4 -1 6 1 4 α 1 HypergeometricPFQ α 4 -1 1 4 α 4 -1 1 4 α 4 -1 3 4 α 4 -1 3 4 1 2 3 4 5 4 -1 p 4 α 0 p -1 1 2 1 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["t_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "p_"]], " ", "t_"]]], " ", RowBox[List["KelvinKer", "[", "t_", "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "3"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "3"]], "+", "\[Alpha]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "p", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox[RowBox[List["1", "+", "\[Alpha]"]], "2"], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List["1", "+", "\[Alpha]"]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["p", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "\[Alpha]"]], ")"]], "2"], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["\[Pi]", " ", "\[Alpha]"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]]]], ")"]]]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["\[Alpha]", "2"], "]"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Alpha]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", FractionBox["\[Alpha]", "4"], ",", FractionBox["\[Alpha]", "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["p", "2"], " ", SuperscriptBox["\[Alpha]", "2"], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "\[Alpha]"]], "4"], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Alpha]", "4"]]], ",", RowBox[List["1", "+", FractionBox["\[Alpha]", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", SuperscriptBox["p", "4"]]]]], "]"]]]]]], ")"]]]]]], ")"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Re", "[", "\[Alpha]", "]"]], ">", "0"]], "&&", RowBox[List[RowBox[List["Re", "[", "p", "]"]], ">", RowBox[List["-", FractionBox["1", SqrtBox["2"]]]]]]]]]]]]]]

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

 2007-05-02