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 KelvinKer

 http://functions.wolfram.com/03.20.17.0012.01

 Input Form

 KelvinKer[\[Nu], z] == -((12 (-3 + \[Nu]) (-2 + \[Nu]) KelvinKei[-6 + \[Nu], z])/z^2) + (1/z^5) (Sqrt[2] (-3 + \[Nu]) (3 z^4 - 16 z^2 (8 - 6 \[Nu] + \[Nu]^2) - 16 (40 - 78 \[Nu] + 49 \[Nu]^2 - 12 \[Nu]^3 + \[Nu]^4)) KelvinKei[-5 + \[Nu], z]) - ((z^4 - 16 (24 - 50 \[Nu] + 35 \[Nu]^2 - 10 \[Nu]^3 + \[Nu]^4)) KelvinKer[-6 + \[Nu], z])/z^4 + (1/z^5) (Sqrt[2] (-3 + \[Nu]) (-3 z^4 - 16 z^2 (8 - 6 \[Nu] + \[Nu]^2) + 16 (40 - 78 \[Nu] + 49 \[Nu]^2 - 12 \[Nu]^3 + \[Nu]^4)) KelvinKer[-5 + \[Nu], z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "6"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "2"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox["z", "5"]], RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["6", " ", "\[Nu]"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]]]], "-", RowBox[List["16", " ", RowBox[List["(", RowBox[List["40", "-", RowBox[List["78", " ", "\[Nu]"]], "+", RowBox[List["49", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["12", " ", SuperscriptBox["\[Nu]", "3"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "5"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "4"], "-", RowBox[List["16", " ", RowBox[List["(", RowBox[List["24", "-", RowBox[List["50", " ", "\[Nu]"]], "+", RowBox[List["35", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["10", " ", SuperscriptBox["\[Nu]", "3"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "6"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "4"]], "+", RowBox[List[FractionBox["1", SuperscriptBox["z", "5"]], RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["6", " ", "\[Nu]"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]]]], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List["40", "-", RowBox[List["78", " ", "\[Nu]"]], "+", RowBox[List["49", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["12", " ", SuperscriptBox["\[Nu]", "3"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "5"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]]]]]]]]]]

 MathML Form

 ker ν ( z ) - 12 ( ν - 3 ) ( ν - 2 ) z 2 kei ν - 6 ( z ) + 2 ( ν - 3 ) ( 3 z 4 - 16 ( ν 2 - 6 ν + 8 ) z 2 - 16 ( ν 4 - 12 ν 3 + 49 ν 2 - 78 ν + 40 ) ) z 5 kei ν - 5 ( z ) + 2 ( ν - 3 ) ( - 3 z 4 - 16 ( ν 2 - 6 ν + 8 ) z 2 + 16 ( ν 4 - 12 ν 3 + 49 ν 2 - 78 ν + 40 ) ) z 5 ker ν - 5 ( z ) - ( z 4 - 16 ( ν 4 - 10 ν 3 + 35 ν 2 - 50 ν + 24 ) ) z 4 ker ν - 6 ( z ) KelvinKer ν z -1 12 ν -3 ν -2 z 2 -1 KelvinKei ν -6 z 2 1 2 ν -3 3 z 4 -1 16 ν 2 -1 6 ν 8 z 2 -1 16 ν 4 -1 12 ν 3 49 ν 2 -1 78 ν 40 z 5 -1 KelvinKei ν -5 z 2 1 2 ν -3 -3 z 4 -1 16 ν 2 -1 6 ν 8 z 2 16 ν 4 -1 12 ν 3 49 ν 2 -1 78 ν 40 z 5 -1 KelvinKer ν -5 z -1 z 4 -1 16 ν 4 -1 10 ν 3 35 ν 2 -1 50 ν 24 z 4 -1 KelvinKer ν -6 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["12", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "6"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "2"]]]], "+", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["6", " ", "\[Nu]"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]]]], "-", RowBox[List["16", " ", RowBox[List["(", RowBox[List["40", "-", RowBox[List["78", " ", "\[Nu]"]], "+", RowBox[List["49", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["12", " ", SuperscriptBox["\[Nu]", "3"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "5"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "5"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", "4"], "-", RowBox[List["16", " ", RowBox[List["(", RowBox[List["24", "-", RowBox[List["50", " ", "\[Nu]"]], "+", RowBox[List["35", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["10", " ", SuperscriptBox["\[Nu]", "3"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "6"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "4"]], "+", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SuperscriptBox["z", "4"]]], "-", RowBox[List["16", " ", SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["8", "-", RowBox[List["6", " ", "\[Nu]"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]]]], "+", RowBox[List["16", " ", RowBox[List["(", RowBox[List["40", "-", RowBox[List["78", " ", "\[Nu]"]], "+", RowBox[List["49", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["12", " ", SuperscriptBox["\[Nu]", "3"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "5"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], SuperscriptBox["z", "5"]]]]]]]]

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

 2007-05-02