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/03.20.06.0030.01

 Input Form

 KelvinKer[\[Nu], z] == (Pi^2 z^Abs[\[Nu]] Sin[(1/4) Pi (2 \[Nu] + Abs[\[Nu]])] HypergeometricPFQRegularized[{}, {1/2, 1/2 + Abs[\[Nu]]/2, 1 + Abs[\[Nu]]/2}, -(z^4/256)])/2^(2 (1 + Abs[\[Nu]])) + (Pi^2 z^(2 + Abs[\[Nu]]) Cos[(1/4) Pi (2 \[Nu] + Abs[\[Nu]])] HypergeometricPFQRegularized[{}, {3/2, 1 + Abs[\[Nu]]/2, 3/2 + Abs[\[Nu]]/2}, -(z^4/256)])/2^(2 (3 + Abs[\[Nu]])) + ((1/4) Sum[(((E^((I Pi (2 \[Nu] + Abs[\[Nu]]))/4) + (-1)^k/E^((I Pi (2 \[Nu] + Abs[\[Nu]]))/4)) (Abs[\[Nu]] - k - 1)!)/ k!) ((I z^2)/4)^k, {k, 0, Abs[\[Nu]] - 1}])/(z/2)^Abs[\[Nu]] - (1/4) ((I z)/2)^Abs[\[Nu]] E^((I Pi \[Nu])/2) Sum[((E^(-((I Pi Abs[\[Nu]])/4)) + (-1)^k E^((I Pi Abs[\[Nu]])/4))/ (k! (k + Abs[\[Nu]])!)) (2 Log[z/2] - PolyGamma[1 + k] - PolyGamma[1 + k + Abs[\[Nu]]]) ((I z^2)/4)^k, {k, 0, Infinity}] /; Element[\[Nu], Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["Abs", "[", "\[Nu]", "]"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["2", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]], " ", "+", " ", RowBox[List[FractionBox["1", "4"], SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "1"]]], RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], "4"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], "4"], " "]]]]]]], ")"]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "k", "-", "1"]], ")"]], "!"]], " "]], RowBox[List["k", "!"]]], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"], ")"]], "k"]]]]]]], "-", RowBox[List[FractionBox["1", "4"], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], ")"]], RowBox[List["Abs", "[", "\[Nu]", "]"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], "4"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], "4"]]]]]], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", RowBox[List["Log", "[", FractionBox["z", "2"], "]"]]]], "-", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "k"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "k", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], "]"]]]], ")"]], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"], ")"]], "k"]]]]]]]]]]], "/;", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]

 MathML Form

 ker ν ( z ) 2 - 2 ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" + 3 ) π 2 z "\[LeftBracketingBar]" ν "\[RightBracketingBar]" + 2 cos ( 1 4 π ( 2 ν + "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) ) 0 F ~ 3 ( ; 3 2 , ν 2 + 1 , ν 2 + 3 2 ; - z 4 256 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["\[LeftBracketingBar]", "\[Nu]", "\[RightBracketingBar]"]], "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["\[LeftBracketingBar]", "\[Nu]", "\[RightBracketingBar]"]], "2"], "+", FractionBox["3", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] + 2 - 2 ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" + 1 ) π 2 z "\[LeftBracketingBar]" ν "\[RightBracketingBar]" sin ( 1 4 π ( 2 ν + "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) ) 0 F ~ 3 ( ; 1 2 , ν 2 + 1 2 , ν 2 + 1 ; - z 4 256 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["\[LeftBracketingBar]", "\[Nu]", "\[RightBracketingBar]"]], "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["\[LeftBracketingBar]", "\[Nu]", "\[RightBracketingBar]"]], "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] + 1 4 ( z 2 ) - "\[LeftBracketingBar]" ν "\[RightBracketingBar]" k = 0 "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - 1 ( ( 1 4 π ( 2 ν + "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) + ( - 1 ) k - 1 4 ( π ( 2 ν + "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) ) ) ( "\[LeftBracketingBar]" ν "\[RightBracketingBar]" - k - 1 ) ! k ! ( z 2 4 ) k - 1 4 ( z 2 ) "\[LeftBracketingBar]" ν "\[RightBracketingBar]" π ν 2 k = 0 ( - 1 4 ( π "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) + ( - 1 ) k 1 4 π "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) ( 2 log ( z 2 ) - ψ TagBox["\[Psi]", PolyGamma] ( k + 1 ) - ψ TagBox["\[Psi]", PolyGamma] ( k + "\[LeftBracketingBar]" ν "\[RightBracketingBar]" + 1 ) ) k ! ( k + "\[LeftBracketingBar]" ν "\[RightBracketingBar]" ) ! ( z 2 4 ) k /; ν TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] FormBox RowBox RowBox RowBox SubscriptBox ker ν ( z ) RowBox RowBox SuperscriptBox 2 RowBox RowBox - 2 RowBox ( RowBox RowBox ν + 3 ) SuperscriptBox π 2 SuperscriptBox z RowBox RowBox ν + 2 RowBox cos ( RowBox FractionBox 1 4 π RowBox ( RowBox RowBox 2 ν + RowBox ν ) ) TagBox TagBox RowBox RowBox SubscriptBox 0 SubscriptBox OverscriptBox F ~ 3 RowBox ( RowBox TagBox TagBox InterpretTemplate Function SlotSequence 1 HypergeometricPFQRegularized Rule Editable Rule Selectable ; TagBox TagBox RowBox TagBox FractionBox 3 2 HypergeometricPFQRegularized Rule Editable Rule Selectable , TagBox RowBox FractionBox RowBox ν 2 + 1 HypergeometricPFQRegularized Rule Editable Rule Selectable , TagBox RowBox FractionBox RowBox ν 2 + FractionBox 3 2 HypergeometricPFQRegularized Rule Editable Rule Selectable InterpretTemplate Function SlotSequence 1 HypergeometricPFQRegularized Rule Editable Rule Selectable ; TagBox RowBox - FractionBox SuperscriptBox z 4 256 HypergeometricPFQRegularized Rule Editable Rule Selectable ) InterpretTemplate Function HypergeometricPFQRegularized Slot 1 Slot 2 Slot 3 Rule Editable Rule Selectable HypergeometricPFQRegularized + RowBox SuperscriptBox 2 RowBox RowBox - 2 RowBox ( RowBox RowBox ν + 1 ) SuperscriptBox π 2 SuperscriptBox z RowBox ν RowBox sin ( RowBox FractionBox 1 4 π RowBox ( RowBox RowBox 2 ν + RowBox ν ) ) TagBox TagBox RowBox RowBox SubscriptBox 0 SubscriptBox OverscriptBox F ~ 3 RowBox ( RowBox TagBox TagBox InterpretTemplate Function SlotSequence 1 HypergeometricPFQRegularized Rule Editable Rule Selectable ; TagBox TagBox RowBox TagBox FractionBox 1 2 HypergeometricPFQRegularized Rule Editable Rule Selectable , TagBox RowBox FractionBox RowBox ν 2 + FractionBox 1 2 HypergeometricPFQRegularized Rule Editable Rule Selectable , TagBox RowBox FractionBox RowBox ν 2 + 1 HypergeometricPFQRegularized Rule Editable Rule Selectable InterpretTemplate Function SlotSequence 1 HypergeometricPFQRegularized Rule Editable Rule Selectable ; TagBox RowBox - FractionBox SuperscriptBox z 4 256 HypergeometricPFQRegularized Rule Editable Rule Selectable ) InterpretTemplate Function HypergeometricPFQRegularized Slot 1 Slot 2 Slot 3 Rule Editable Rule Selectable HypergeometricPFQRegularized + RowBox FractionBox 1 4 SuperscriptBox RowBox ( FractionBox z 2 ) RowBox - RowBox ν RowBox UnderoverscriptBox RowBox k = 0 RowBox RowBox ν - 1 ErrorBox RowBox FractionBox RowBox ( RowBox RowBox ( RowBox SuperscriptBox RowBox FractionBox 1 4 π RowBox ( RowBox RowBox 2 ν + RowBox ν ) + RowBox SuperscriptBox RowBox ( RowBox - 1 ) k SuperscriptBox RowBox RowBox - FractionBox 1 4 RowBox ( RowBox π RowBox ( RowBox RowBox 2 ν + RowBox ν ) ) ) RowBox RowBox ( RowBox RowBox ν - k - 1 ) ! RowBox k ! SuperscriptBox RowBox ( FractionBox RowBox SuperscriptBox z 2 4 ) k - RowBox FractionBox 1 4 SuperscriptBox RowBox ( FractionBox RowBox z 2 ) RowBox ν SuperscriptBox FractionBox RowBox π ν 2 RowBox UnderoverscriptBox RowBox k = 0 RowBox FractionBox RowBox RowBox ( RowBox SuperscriptBox RowBox RowBox - FractionBox 1 4 RowBox ( RowBox π RowBox ν ) + RowBox SuperscriptBox RowBox ( RowBox - 1 ) k SuperscriptBox RowBox FractionBox 1 4 π RowBox ν ) RowBox ( RowBox RowBox 2 RowBox log ( FractionBox z 2 ) - RowBox TagBox ψ PolyGamma ( RowBox k + 1 ) - RowBox TagBox ψ PolyGamma ( RowBox k + RowBox ν + 1 ) ) RowBox RowBox k ! RowBox RowBox ( RowBox k + RowBox ν ) ! SuperscriptBox RowBox ( FractionBox RowBox SuperscriptBox z 2 4 ) k /; RowBox ν TagBox Function TraditionalForm [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["Abs", "[", "\[Nu]", "]"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]]], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["z", RowBox[List["2", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], "]"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]], ",", RowBox[List[FractionBox["3", "2"], "+", FractionBox[RowBox[List["Abs", "[", "\[Nu]", "]"]], "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "256"]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["-", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "1"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]], ")"]]]]]]]]], ")"]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "\[Nu]", "]"]], "-", "k", "-", "1"]], ")"]], "!"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]], "-", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], ")"]], RowBox[List["Abs", "[", "\[Nu]", "]"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox["1", "4"], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", RowBox[List["Abs", "[", "\[Nu]", "]"]]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["Log", "[", FractionBox["z", "2"], "]"]]]], "-", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "k"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "k", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]], "4"], ")"]], "k"]]], RowBox[List[RowBox[List["k", "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "+", RowBox[List["Abs", "[", "\[Nu]", "]"]]]], ")"]], "!"]]]]]]]]]]], "/;", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]

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

 2007-05-02