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/03.16.06.0033.01

 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))))) ((Sqrt[(-1)^(3/4) z] (-((Pi (I Sqrt[2] E^(I Sqrt[2] z) z + (1 + I) E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z + Sqrt[(-I) z^2])))/ Sqrt[2]) + 4 (E^(I Sqrt[2] z) z - (-1)^(3/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])) + Sqrt[(-(-1)^(1/4)) z] (Pi (4 z - 3 I E^((1 + I) Sqrt[2] z) z + ((3 - 3 I) Sqrt[I z^2])/Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) HypergeometricPFQ[{1/8, 1/8, 3/8, 3/8, 5/8, 5/8, 7/8, 7/8}, {1/4, 1/2, 3/4}, -(16/z^4)] - ((-1)^(3/4)/(8 z)) (Sqrt[(-1)^(3/4) z] ((1/2) (-2 E^(I Sqrt[2] z) Pi z + (1 + I) E^(Sqrt[2] z) Pi ((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2])) + 4 ((-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])) + Sqrt[(-(-1)^(1/4)) z] (Pi (-4 z - 3 I E^(2 (-1)^(1/4) z) z + 3 (-1)^(3/4) Sqrt[I z^2]) + 4 (E^((1 + I) Sqrt[2] z) z - (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {3/8, 3/8, 5/8, 5/8, 7/8, 7/8, 9/8, 9/8}, {1/2, 3/4, 5/4}, -(16/z^4)] + ((9 I)/(128 z^2)) (Sqrt[(-1)^(3/4) z] (-((Pi (I Sqrt[2] E^(I Sqrt[2] z) z + (1 + I) E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z + Sqrt[(-I) z^2])))/Sqrt[2]) + 4 (E^(I Sqrt[2] z) z - (-1)^(3/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])) - Sqrt[(-(-1)^(1/4)) z] (Pi (4 z - 3 I E^((1 + I) Sqrt[2] z) z + ((3 - 3 I) Sqrt[I z^2])/ Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {5/8, 5/8, 7/8, 7/8, 9/8, 9/8, 11/8, 11/8}, {3/4, 5/4, 3/2}, -(16/z^4)] + ((75 (-1)^(1/4))/(1024 z^3)) (Sqrt[(-1)^(3/4) z] ((1/2) (-2 E^(I Sqrt[2] z) Pi z + (1 + I) E^(Sqrt[2] z) Pi ((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2])) + 4 ((-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])) - Sqrt[(-(-1)^(1/4)) z] (Pi (-4 z - 3 I E^(2 (-1)^(1/4) z) z + 3 (-1)^(3/4) Sqrt[I z^2]) + 4 (E^((1 + I) Sqrt[2] z) z - (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) HypergeometricPFQ[ {7/8, 7/8, 9/8, 9/8, 11/8, 11/8, 13/8, 13/8}, {5/4, 3/2, 7/4}, -(16/z^4)]) /; (Abs[z] -> Infinity)

 Standard Form

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 MathML Form

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( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) [/itex]

 Rule Form

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

 2007-05-02