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/03.20.06.0038.01

 Input Form

 KelvinKer[\[Nu], z] \[Proportional] (Sqrt[Pi]/(E^(z/Sqrt[2]) Sqrt[2 z])) (Cos[(1/8) (Pi (1 + 4 \[Nu]) + 4 Sqrt[2] z)] HypergeometricPFQ[ {(1 - 2 \[Nu])/8, (3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (1 + 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8}, {1/4, 1/2, 3/4}, -(16/z^4)] - ((9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2)) Sin[(1/8) (Pi (1 + 4 \[Nu]) + 4 Sqrt[2] z)] HypergeometricPFQ[ {(5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8}, {3/4, 5/4, 3/2}, -(16/z^4)] - ((1 - 4 \[Nu]^2)/(8 z)) Sin[(1/8) (Pi (1 - 4 \[Nu]) - 4 Sqrt[2] z)] HypergeometricPFQ[ {(3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8}, {1/2, 3/4, 5/4}, -(16/z^4)] + ((225 - 1036 \[Nu]^2 + 560 \[Nu]^4 - 64 \[Nu]^6)/(3072 z^3)) Cos[(1/8) (Pi (1 - 4 \[Nu]) - 4 Sqrt[2] z)] HypergeometricPFQ[ {(7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (13 - 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8, (13 + 2 \[Nu])/8}, {5/4, 3/2, 7/4}, -(16/z^4)]) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]]]], RowBox[List[SqrtBox[RowBox[List["2", "z"]]], " "]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["3", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["1", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], ",", FractionBox["1", "2"], ",", FractionBox["3", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "4"], ",", FractionBox["5", "4"], ",", FractionBox["3", "2"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], RowBox[List["8", "z"]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["3", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["5", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "+", RowBox[List["2", "\[Nu]"]]]], "8"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", FractionBox["3", "4"], ",", FractionBox["5", "4"]]], "}"]], ",", RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["225", "-", RowBox[List["1036", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["560", " ", SuperscriptBox["\[Nu]", "4"]]], "-", RowBox[List["64", " ", SuperscriptBox["\[Nu]", "6"]]]]], RowBox[List["3072", " ", SuperscriptBox["z", "3"]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", RowBox[List["(", RowBox[List["1", "-", RowBox[List["4", " ", "\[Nu]"]]]], ")"]]]], "-", RowBox[List["4", " ", SqrtBox["2"], " ", "z"]]]], ")"]]]], "]"]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["7", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["13", "-", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["7", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["9", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["11", "+", RowBox[List["2", "\[Nu]"]]]], "8"], ",", FractionBox[RowBox[List["13", "+", RowBox[List["2", "\[Nu]"]]]], "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["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 ker ν ( z ) π - z 2 2 z ( cos ( 1 8 ( 4 2 z + π ( 4 ν + 1 ) ) ) 8 F 3 ( 1 8 ( 1 - 2 ν ) , 1 8 ( 3 - 2 ν ) , 1 8 ( 5 - 2 ν ) , 1 8 ( 7 - 2 ν ) , 1 8 ( 2 ν + 1 ) , 1 8 ( 2 ν + 3 ) , 1 8 ( 2 ν + 5 ) , 1 8 ( 2 ν + 7 ) ; 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[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "1"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 1 - 4 ν 2 8 z sin ( 1 8 ( π ( 1 - 4 ν ) - 4 2 z ) ) 8 F 3 ( 1 8 ( 3 - 2 ν ) , 1 8 ( 5 - 2 ν ) , 1 8 ( 7 - 2 ν ) , 1 8 ( 9 - 2 ν ) , 1 8 ( 2 ν + 3 ) , 1 8 ( 2 ν + 5 ) , 1 8 ( 2 ν + 7 ) , 1 8 ( 2 ν + 9 ) ; 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[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - 16 ν 4 - 40 ν 2 + 9 128 z 2 sin ( 1 8 ( 4 2 z + π ( 4 ν + 1 ) ) ) 8 F 3 ( 1 8 ( 5 - 2 ν ) , 1 8 ( 7 - 2 ν ) , 1 8 ( 9 - 2 ν ) , 1 8 ( 11 - 2 ν ) , 1 8 ( 2 ν + 5 ) , 1 8 ( 2 ν + 7 ) , 1 8 ( 2 ν + 9 ) , 1 8 ( 2 ν + 11 ) ; 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[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "11"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + - 64 ν 6 + 560 ν 4 - 1036 ν 2 + 225 3072 z 3 cos ( 1 8 ( π ( 1 - 4 ν ) - 4 2 z ) ) 8 F 3 ( 1 8 ( 7 - 2 ν ) , 1 8 ( 9 - 2 ν ) , 1 8 ( 11 - 2 ν ) , 1 8 ( 13 - 2 ν ) , 1 8 ( 2 ν + 7 ) , 1 8 ( 2 ν + 9 ) , 1 8 ( 2 ν + 11 ) , 1 8 ( 2 ν + 13 ) ; 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[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["13", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "11"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "13"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinKer ν z 1 2 -1 z 2 1 2 -1 2 z 1 2 -1 1 8 4 2 1 2 z 4 ν 1 HypergeometricPFQ 1 8 1 -1 2 ν 1 8 3 -1 2 ν 1 8 5 -1 2 ν 1 8 7 -1 2 ν 1 8 2 ν 1 1 8 2 ν 3 1 8 2 ν 5 1 8 2 ν 7 1 4 1 2 3 4 -1 16 z 4 -1 -1 1 -1 4 ν 2 8 z -1 1 8 1 -1 4 ν -1 4 2 1 2 z HypergeometricPFQ 1 8 3 -1 2 ν 1 8 5 -1 2 ν 1 8 7 -1 2 ν 1 8 9 -1 2 ν 1 8 2 ν 3 1 8 2 ν 5 1 8 2 ν 7 1 8 2 ν 9 1 2 3 4 5 4 -1 16 z 4 -1 -1 16 ν 4 -1 40 ν 2 9 128 z 2 -1 1 8 4 2 1 2 z 4 ν 1 HypergeometricPFQ 1 8 5 -1 2 ν 1 8 7 -1 2 ν 1 8 9 -1 2 ν 1 8 11 -1 2 ν 1 8 2 ν 5 1 8 2 ν 7 1 8 2 ν 9 1 8 2 ν 11 3 4 5 4 3 2 -1 16 z 4 -1 -64 ν 6 560 ν 4 -1 1036 ν 2 225 3072 z 3 -1 1 8 1 -1 4 ν -1 4 2 1 2 z HypergeometricPFQ 1 8 7 -1 2 ν 1 8 9 -1 2 ν 1 8 11 -1 2 ν 1 8 13 -1 2 ν 1 8 2 ν 7 1 8 2 ν 9 1 8 2 ν 11 1 8 2 ν 13 5 4 3 2 7 4 -1 16 z 4 -1 Rule z [/itex]

 Rule Form

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

 2007-05-02