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 KelvinBei

 http://functions.wolfram.com/03.17.13.0007.01

 Input Form

 z^4 Derivative[4][w][z] + (6 - 4 r - 4 s) z^3 Derivative[3][w][z] + z^2 (7 + 12 r (-1 + s) + 6 (-2 + s) s - 2 r^2 (-2 + \[Nu]^2)) Derivative[2][w][z] + (-1 + 2 r + 2 s) z (-1 + r (2 - 4 s) - 2 (-1 + s) s + 2 r^2 \[Nu]^2) Derivative[1][w][z] + (4 r s^3 + s^4 - 4 r^3 s \[Nu]^2 - 2 r^2 s^2 (-2 + \[Nu]^2) + r^4 (a^4 z^(4 r) - 4 \[Nu]^2 + \[Nu]^4)) w[z] == 0 /; w[z] == Subscript[c, 1] z^s KelvinBer[\[Nu], a z^r] + Subscript[c, 2] z^s KelvinBei[\[Nu], a z^r] + Subscript[c, 3] z^s KelvinKer[\[Nu], a z^r] + Subscript[c, 4] z^s KelvinKei[\[Nu], a z^r]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["z", "4"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["6", "-", RowBox[List["4", " ", "r"]], "-", RowBox[List["4", " ", "s"]]]], ")"]], SuperscriptBox["z", "3"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["12", " ", "r", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "s"]], ")"]]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "s"]], ")"]], " ", "s"]], "-", RowBox[List["2", " ", SuperscriptBox["r", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "r"]], "+", RowBox[List["2", " ", "s"]]]], ")"]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["r", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["4", " ", "s"]]]], ")"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "s"]], ")"]], " ", "s"]], "+", RowBox[List["2", " ", SuperscriptBox["r", "2"], " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", "r", " ", SuperscriptBox["s", "3"]]], "+", SuperscriptBox["s", "4"], "-", RowBox[List["4", " ", SuperscriptBox["r", "3"], " ", "s", " ", SuperscriptBox["\[Nu]", "2"]]], "-", RowBox[List["2", " ", SuperscriptBox["r", "2"], " ", SuperscriptBox["s", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", SuperscriptBox["\[Nu]", "2"]]], ")"]]]], "+", RowBox[List[SuperscriptBox["r", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", RowBox[List["4", " ", "r"]]]]], "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]], "+", SuperscriptBox["\[Nu]", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["w", "[", "z", "]"]]]]]], " ", "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], SuperscriptBox["z", "s"], RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], SuperscriptBox["z", "s"], RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "3"], SuperscriptBox["z", "s"], RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "4"], SuperscriptBox["z", "s"], RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]]]]]]]]

 MathML Form

 z 4 w ( 4 ) TagBox[RowBox[List["(", "4", ")"]], Derivative] ( z ) + ( 6 - 4 r - 4 s ) z 3 w ( 3 ) TagBox[RowBox[List["(", "3", ")"]], Derivative] ( z ) + ( 7 - 2 ( ν 2 - 2 ) r 2 + 12 ( s - 1 ) r + 6 ( s - 2 ) s ) z 2 w ′′ ( z ) + ( 2 r + 2 s - 1 ) ( 2 r 2 ν 2 - 2 ( s - 1 ) s + r ( 2 - 4 s ) - 1 ) z w ( z ) + ( ( a 4 z 4 r + ν 4 - 4 ν 2 ) r 4 - 4 s ν 2 r 3 - 2 s 2 ( ν 2 - 2 ) r 2 + 4 s 3 r + s 4 ) w ( z ) 0 /; w ( z ) c 1 z s ber ν ( a z r ) + c 2 z s bei ν ( a z r ) + c 3 z s ker ν ( a z r ) + c 4 z s kei ν ( a z r ) Condition z 4 z 4 w z 6 -1 4 r -1 4 s z 3 z 3 w z 7 -1 2 ν 2 -2 r 2 12 s -1 r 6 s -2 s z 2 z 2 w z 2 r 2 s -1 2 r 2 ν 2 -1 2 s -1 s r 2 -1 4 s -1 z z w z a 4 z 4 r ν 4 -1 4 ν 2 r 4 -1 4 s ν 2 r 3 -1 2 s 2 ν 2 -2 r 2 4 s 3 r s 4 w z 0 w z Subscript c 1 z s KelvinBer ν a z r Subscript c 2 z s KelvinBei ν a z r Subscript c 3 z s KelvinKer ν a z r Subscript c 4 z s KelvinKei ν a z r [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["z_", "4"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "4", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["6", "-", RowBox[List["4", " ", "r_"]], "-", RowBox[List["4", " ", "s_"]]]], ")"]], " ", SuperscriptBox["z_", "3"], " ", RowBox[List[SuperscriptBox["w", TagBox[RowBox[List["(", "3", ")"]], Derivative], Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[SuperscriptBox["z_", "2"], " ", RowBox[List["(", RowBox[List["7", "+", RowBox[List["12", " ", "r_", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "s_"]], ")"]]]], "+", RowBox[List["6", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "s_"]], ")"]], " ", "s_"]], "-", RowBox[List["2", " ", SuperscriptBox["r_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", SuperscriptBox["\[Nu]_", "2"]]], ")"]]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "r_"]], "+", RowBox[List["2", " ", "s_"]]]], ")"]], " ", "z_", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["r_", " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["4", " ", "s_"]]]], ")"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "s_"]], ")"]], " ", "s_"]], "+", RowBox[List["2", " ", SuperscriptBox["r_", "2"], " ", SuperscriptBox["\[Nu]_", "2"]]]]], ")"]], " ", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "z_", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", "r_", " ", SuperscriptBox["s_", "3"]]], "+", SuperscriptBox["s_", "4"], "-", RowBox[List["4", " ", SuperscriptBox["r_", "3"], " ", "s_", " ", SuperscriptBox["\[Nu]_", "2"]]], "-", RowBox[List["2", " ", SuperscriptBox["r_", "2"], " ", SuperscriptBox["s_", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", SuperscriptBox["\[Nu]_", "2"]]], ")"]]]], "+", RowBox[List[SuperscriptBox["r_", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["a_", "4"], " ", SuperscriptBox["z_", RowBox[List["4", " ", "r_"]]]]], "-", RowBox[List["4", " ", SuperscriptBox["\[Nu]_", "2"]]], "+", SuperscriptBox["\[Nu]_", "4"]]], ")"]]]]]], ")"]], " ", RowBox[List["w", "[", "z_", "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List[SubscriptBox["c", "1"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "2"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["KelvinBei", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "3"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List[SubscriptBox["c", "4"], " ", SuperscriptBox["z", "s"], " ", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]]]]]]]]]]]]

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.