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/03.14.06.0024.01

 Input Form

 KelvinBer[z] \[Proportional] (1/(Sqrt[2 Pi] Sqrt[z])) ((E^(z/Sqrt[2]) Cos[(1/8) (Pi - 4 Sqrt[2] z)] + (I Sin[(1/8) (3 Pi - 4 Sqrt[2] z)])/E^(z/Sqrt[2])) HypergeometricPFQ[{1/8, 1/8, 3/8, 3/8, 5/8, 5/8, 7/8, 7/8}, {1/4, 1/2, 3/4}, -(16/z^4)] + (1/(8 z)) (E^(z/Sqrt[2]) Sin[(1/8) (Pi + 4 Sqrt[2] z)] + (I Sin[(1/8) (-Pi + 4 Sqrt[2] z)])/E^(z/Sqrt[2])) HypergeometricPFQ[{3/8, 3/8, 5/8, 5/8, 7/8, 7/8, 9/8, 9/8}, {1/2, 3/4, 5/4}, -(16/z^4)] - (9/(128 z^2)) (E^(z/Sqrt[2]) Sin[(1/8) (Pi - 4 Sqrt[2] z)] + (I Cos[(1/8) (3 Pi - 4 Sqrt[2] z)])/E^(z/Sqrt[2])) HypergeometricPFQ[{5/8, 5/8, 7/8, 7/8, 9/8, 9/8, 11/8, 11/8}, {3/4, 5/4, 3/2}, -(16/z^4)] - (75/(1024 z^3)) (E^(z/Sqrt[2]) Cos[(1/8) (Pi + 4 Sqrt[2] z)] - (I Cos[(1/8) (-Pi + 4 Sqrt[2] z)])/E^(z/Sqrt[2])) HypergeometricPFQ[{7/8, 7/8, 9/8, 9/8, 11/8, 11/8, 13/8, 13/8}, {5/4, 3/2, 7/4}, -(16/z^4)]) /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi] && (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox["1", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox["z"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[Pi]"]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["8", " ", "z"]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox["9", RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[Pi]"]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox["75", RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"], ",", FractionBox["13", "8"], ",", FractionBox["13", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

 MathML Form

 ber ( z ) 1 2 π z ( ( z 2 cos ( 1 8 ( π - 4 2 z ) ) + - z 2 sin ( 1 8 ( 3 π - 4 2 z ) ) ) 8 F 3 ( 1 8 , 1 8 , 3 8 , 3 8 , 5 8 , 5 8 , 7 8 , 7 8 ; 1 4 , 1 2 , 3 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], 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["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] + 1 8 z ( z 2 sin ( 1 8 ( 4 2 z + π ) ) + - z 2 sin ( 1 8 ( 4 2 z - π ) ) ) 8 F 3 ( 3 8 , 3 8 , 5 8 , 5 8 , 7 8 , 7 8 , 9 8 , 9 8 ; 1 2 , 3 4 , 5 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], 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["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 9 128 z 2 ( z 2 sin ( 1 8 ( π - 4 2 z ) ) + - z 2 cos ( 1 8 ( 3 π - 4 2 z ) ) ) 8 F 3 ( 5 8 , 5 8 , 7 8 , 7 8 , 9 8 , 9 8 , 11 8 , 11 8 ; 3 4 , 5 4 , 3 2 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], 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["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 75 1024 z 3 ( z 2 cos ( 1 8 ( 4 2 z + π ) ) - - z 2 cos ( 1 8 ( 4 2 z - π ) ) ) 8 F 3 ( 7 8 , 7 8 , 9 8 , 9 8 , 11 8 , 11 8 , 13 8 , 13 8 ; 5 4 , 3 2 , 7 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["9", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["11", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["13", "8"], 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["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ) /; - π 2 < arg ( z ) π ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinBer z 1 2 1 2 z 1 2 -1 z 2 1 2 -1 1 8 -1 4 2 1 2 z -1 z 2 1 2 -1 1 8 3 -1 4 2 1 2 z HypergeometricPFQ 1 8 1 8 3 8 3 8 5 8 5 8 7 8 7 8 1 4 1 2 3 4 -1 16 z 4 -1 1 8 z -1 z 2 1 2 -1 1 8 4 2 1 2 z -1 z 2 1 2 -1 1 8 4 2 1 2 z -1 HypergeometricPFQ 3 8 3 8 5 8 5 8 7 8 7 8 9 8 9 8 1 2 3 4 5 4 -1 16 z 4 -1 -1 9 128 z 2 -1 z 2 1 2 -1 1 8 -1 4 2 1 2 z -1 z 2 1 2 -1 1 8 3 -1 4 2 1 2 z HypergeometricPFQ 5 8 5 8 7 8 7 8 9 8 9 8 11 8 11 8 3 4 5 4 3 2 -1 16 z 4 -1 -1 75 1024 z 3 -1 z 2 1 2 -1 1 8 4 2 1 2 z -1 -1 z 2 1 2 -1 1 8 4 2 1 2 z -1 HypergeometricPFQ 7 8 7 8 9 8 9 8 11 8 11 8 13 8 13 8 5 4 3 2 7 4 -1 16 z 4 -1 Inequality -1 2 -1 z Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBer", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[Pi]"]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "8"], ",", FractionBox["1", "8"], ",", FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["3", "8"], ",", FractionBox["3", "8"], ",", FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["8", " ", "z"]]], "-", FractionBox[RowBox[List["9", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "\[Pi]"]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["5", "8"], ",", FractionBox["5", "8"], ",", FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List["75", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["\[Pi]", "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]]]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["7", "8"], ",", FractionBox["7", "8"], ",", FractionBox["9", "8"], ",", FractionBox["9", "8"], ",", FractionBox["11", "8"], ",", FractionBox["11", "8"], ",", FractionBox["13", "8"], ",", FractionBox["13", "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "4"], ",", FractionBox["3", "2"], ",", FractionBox["7", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]]]], RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox["z"]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]

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

 2007-05-02