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/03.18.20.0006.01

 Input Form

 Derivative[1, 0][KelvinBer][n + 1/2, z] == (-((3 Pi)/4)) KelvinBei[1/2 + n, z] + (Log[z] - Log[(-1)^(1/4) z]) KelvinBer[1/2 + n, z] + (((-1)^(3/8) 2^(-(1/2) - n) E^((3 I n Pi)/4) z^(-(1/2) - n))/(n! Sqrt[Pi])) Sum[2^(2 k) Binomial[n, 2 k] (2 n - 2 k)! I^k (E^((3 Pi I)/4) I^n ((-(CoshIntegral[2 (-1)^(1/4) z] - PolyGamma[1/2 + k] + PolyGamma[1/2 + k - n])) Sinh[(-1)^(1/4) z] + Cosh[(-1)^(1/4) z] SinhIntegral[2 (-1)^(1/4) z]) + (-1)^k ((-(CosIntegral[2 (-1)^(1/4) z] - PolyGamma[1/2 + k] + PolyGamma[1/2 + k - n])) Sin[(-1)^(1/4) z] + Cos[(-1)^(1/4) z] SinIntegral[2 (-1)^(1/4) z])) z^(2 k), {k, 0, Floor[n/2]}] + (((-1)^(5/8) 2^(1/2 - n) E^((3 Pi I n)/4) z^(1/2 - n))/(n! Sqrt[Pi])) Sum[2^(2 k) Binomial[n, 2 k + 1] (2 n - 2 k - 1)! I^k ((-1)^(3/4) E^((I n Pi)/2) (Cosh[(-1)^(1/4) z] (CoshIntegral[2 (-1)^(1/4) z] - PolyGamma[3/2 + k] + PolyGamma[1/2 + k - n]) - Sinh[(-1)^(1/4) z] SinhIntegral[2 (-1)^(1/4) z]) + (-1)^k (Cos[(-1)^(1/4) z] (CosIntegral[2 (-1)^(1/4) z] - PolyGamma[3/2 + k] + PolyGamma[1/2 + k - n]) + Sin[(-1)^(1/4) z] SinIntegral[2 (-1)^(1/4) z])) z^(2 k), {k, 0, Floor[(n - 1)/2]}] /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 ber TagBox["ber", BesselJ] n + 1 2 ( 1 , 0 ) TagBox[RowBox[List["(", RowBox[List["1", ",", "0"]], ")"]], Derivative] ( z ) - 3 π 4 bei n + 1 2 ( z ) - ( log ( - 1 4 z ) - log ( z ) ) ber n + 1 2 ( z ) + ( - 1 ) 3 / 8 2 - n - 1 2 3 n π 4 z - n - 1 2 n ! π k = 0 n 2 2 2 k ( n 2 k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[RowBox[List["2", " ", "k"]], Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] ( 2 n - 2 k ) ! k ( ( - 1 ) 3 / 4 n ( cosh ( - 1 4 z ) Shi ( 2 - 1 4 z ) - ( Chi ( 2 - 1 4 z ) - ψ TagBox["\[Psi]", PolyGamma] ( k + 1 2 ) + ψ TagBox["\[Psi]", PolyGamma] ( k - n + 1 2 ) ) sinh ( - 1 4 z ) ) + ( - 1 ) k ( cos ( - 1 4 z ) Si ( 2 - 1 4 z ) - ( Ci ( 2 - 1 4 z ) - ψ TagBox["\[Psi]", PolyGamma] ( k + 1 2 ) + ψ TagBox["\[Psi]", PolyGamma] ( k - n + 1 2 ) ) sin ( - 1 4 z ) ) ) z 2 k + ( - 1 ) 5 / 8 2 1 2 - n 3 n π 4 z 1 2 - n n ! π k = 0 n - 1 2 2 2 k ( n 2 k + 1 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox[RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] ( - 2 k + 2 n - 1 ) ! k ( ( - 1 ) 3 / 4 n π 2 ( cosh ( - 1 4 z ) ( Chi ( 2 - 1 4 z ) - ψ TagBox["\[Psi]", PolyGamma] ( k + 3 2 ) + ψ TagBox["\[Psi]", PolyGamma] ( k - n + 1 2 ) ) - sinh ( - 1 4 z ) Shi ( 2 - 1 4 z ) ) + ( - 1 ) k ( cos ( - 1 4 z ) ( Ci ( 2 - 1 4 z ) - ψ TagBox["\[Psi]", PolyGamma] ( k + 3 2 ) + ψ TagBox["\[Psi]", PolyGamma] ( k - n + 1 2 ) ) + sin ( - 1 4 z ) Si ( 2 - 1 4 z ) ) ) z 2 k /; n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] Condition 1 0 Subscript BesselJ ber n 1 2 z -1 3 4 -1 KelvinBei n 1 2 z -1 -1 1 4 z -1 z KelvinBer n 1 2 z -1 3 8 2 -1 n -1 1 2 3 n 4 -1 z -1 n -1 1 2 n 1 2 -1 k 0 n 2 -1 2 2 k Binomial n 2 k 2 n -1 2 k k -1 3 4 n -1 1 4 z SinhIntegral 2 -1 1 4 z -1 CoshIntegral 2 -1 1 4 z -1 PolyGamma k 1 2 PolyGamma k -1 n 1 2 -1 1 4 z -1 k -1 1 4 z SinIntegral 2 -1 1 4 z -1 CosIntegral 2 -1 1 4 z -1 PolyGamma k 1 2 PolyGamma k -1 n 1 2 -1 1 4 z z 2 k -1 5 8 2 1 2 -1 n 3 n 4 -1 z 1 2 -1 n n 1 2 -1 k 0 n -1 2 -1 2 2 k Binomial n 2 k 1 -2 k 2 n -1 k -1 3 4 n 2 -1 -1 1 4 z CoshIntegral 2 -1 1 4 z -1 PolyGamma k 3 2 PolyGamma k -1 n 1 2 -1 -1 1 4 z SinhIntegral 2 -1 1 4 z -1 k -1 1 4 z CosIntegral 2 -1 1 4 z -1 PolyGamma k 3 2 PolyGamma k -1 n 1 2 -1 1 4 z SinIntegral 2 -1 1 4 z z 2 k n [/itex]

 Rule Form

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

 2007-05-02