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/03.16.06.0032.01

 Input Form

 KelvinKer[z] \[Proportional] (-(1/(E^(((1 + I) z)/Sqrt[2]) (8 Sqrt[2 Pi] Sqrt[(-(-1)^(1/4)) z] ((-1)^(3/4) z)^(3/2))))) (Sum[(Pochhammer[1/2, 2 k]^2/(2 k)!) (I/(4 z^2))^k ((Pi/Sqrt[2]) ((-1)^(3/4 + k) Sqrt[2] (4 - 3 I E^((1 + I) Sqrt[2] z)) ((-(-1)^(1/4)) z)^(3/2) + 3 (1 - I) (-1)^k Sqrt[(-(-1)^(1/4)) z] Sqrt[I z^2] + Sqrt[(-1)^(3/4) z] ((-I) Sqrt[2] E^(I Sqrt[2] z) z - (1 + I) E^(Sqrt[2] z) (2 (-1 + I) Sqrt[2] z + Sqrt[(-I) z^2]))) + 4 Sqrt[(-1)^(3/4) z] (E^(I Sqrt[2] z) z - (-1)^(3/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z]) + 4 (-1)^k Sqrt[(-(-1)^(1/4)) z] (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])), {k, 0, Floor[n/2]}] - ((-1)^(3/4)/(2 z)) Sum[(Pochhammer[1/2, 1 + 2 k]^2/(1 + 2 k)!) (I/(4 z^2))^k (((1 + I)/2) Pi ((-1 + I) (-1)^(3/4 + k) (4 + 3 I E^(2 (-1)^(1/4) z)) ((-(-1)^(1/4)) z)^(3/2) + 3 (1 - I) (-1)^(3/4 + k) Sqrt[(-(-1)^(1/4)) z] Sqrt[I z^2] + Sqrt[(-1)^(3/4) z] ((-1 + I) E^(I Sqrt[2] z) z + E^(Sqrt[2] z) (4 (1 + I) z - I Sqrt[2] Sqrt[(-I) z^2]))) + 4 Sqrt[(-1)^(3/4) z] ((-I) E^(I Sqrt[2] z) z + (-1)^(1/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z]) + 4 (-1)^k Sqrt[(-(-1)^(1/4)) z] (E^((1 + I) Sqrt[2] z) z - (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])), {k, 0, Floor[(n - 1)/2]}] + \[Ellipsis]) /; (Abs[z] -> Infinity) && Element[n, Integers] && n >= 0

 Standard Form

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RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]]]], "+", "\[Ellipsis]"]], " ", ")"]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 ker ( z ) - - ( 1 + ) z 2 8 2 π - - 1 4 z ( ( - 1 ) 3 / 4 z ) 3 / 2 ( k = 0 n 2 1 ( 2 k ) ! ( 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] 2 ( 4 z 2 ) k ( π 2 ( ( - 1 ) k + 3 4 2 ( 4 - 3 ( 1 + ) 2 z ) ( - - 1 4 z ) 3 / 2 + 3 ( - 1 ) k ( 1 - ) z 2 - - 1 4 z + ( - 1 ) 3 / 4 z ( 2 2 z ( - ) z - ( 1 + ) 2 z ( 2 2 ( - 1 + ) z + - z 2 ) ) ) + 4 ( - 1 ) 3 / 4 z ( 2 z z - ( - 1 ) 3 / 4 2 z - z 2 ) ( log ( - - 1 4 z ) - log ( z ) ) + 4 ( - 1 ) k - - 1 4 z ( ( 1 + ) 2 z z + - 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) - ( - 1 ) 3 / 4 2 z k = 0 n - 1 2 1 ( 2 k + 1 ) ! ( 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] 2 ( 4 z 2 ) k ( ( 1 + ) π 2 ( ( - 1 ) k + 3 4 ( 4 + 3 2 - 1 4 z ) ( - 1 + ) ( - - 1 4 z ) 3 / 2 + 3 ( - 1 ) k + 3 4 ( 1 - ) z 2 - - 1 4 z + ( - 1 ) 3 / 4 z ( 2 z ( - 1 + ) z + 2 z ( 4 ( 1 + ) z - 2 - z 2 ) ) ) + 4 ( - 1 ) 3 / 4 z ( - 1 4 2 z - z 2 - 2 z z ) ( log ( - - 1 4 z ) - log ( z ) ) + 4 ( - 1 ) k - - 1 4 z ( ( 1 + ) 2 z z - - 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) + ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) n Condition Proportional KelvinKer z -1 -1 1 z 2 1 2 -1 8 2 1 2 -1 -1 1 4 z 1 2 -1 3 4 z 3 2 -1 k 0 n 2 -1 1 2 k -1 Pochhammer 1 2 2 k 2 4 z 2 -1 k 2 1 2 -1 -1 k 3 4 2 1 2 4 -1 3 1 2 1 2 z -1 -1 1 4 z 3 2 3 -1 k 1 -1 z 2 1 2 -1 -1 1 4 z 1 2 -1 3 4 z 1 2 2 1 2 2 1 2 z -1 z -1 1 2 1 2 z 2 2 1 2 -1 z -1 z 2 1 2 4 -1 3 4 z 1 2 2 1 2 z z -1 -1 3 4 2 1 2 z -1 z 2 1 2 -1 -1 1 4 z -1 z 4 -1 k -1 -1 1 4 z 1 2 1 2 1 2 z z -1 1 4 z 2 1 2 -1 3 4 z -1 z -1 -1 3 4 2 z -1 k 0 n -1 2 -1 1 2 k 1 -1 Pochhammer 1 2 2 k 1 2 4 z 2 -1 k 1 2 -1 -1 k 3 4 4 3 2 -1 1 4 z -1 -1 -1 1 4 z 3 2 3 -1 k 3 4 1 -1 z 2 1 2 -1 -1 1 4 z 1 2 -1 3 4 z 1 2 2 1 2 z -1 z 2 1 2 z 4 1 z -1 2 1 2 -1 z 2 1 2 4 -1 3 4 z 1 2 -1 1 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z -1 -1 1 4 z -1 z 4 -1 k -1 -1 1 4 z 1 2 1 2 1 2 z z -1 -1 1 4 z 2 1 2 -1 3 4 z -1 z Rule z n [/itex]

 Rule Form

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

 2007-05-02