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; }

 Exp

 http://functions.wolfram.com/01.03.15.0005.01

 Input Form

 WignerTransform[Subscript[\[Psi], k][y], y, {x, p}] == (1/4) I Pi Sinh[Pi k] ((E^(2 I (k - p) x) cM HypergeometricPFQRegularized[ {}, {1 + I k, 1 - I p, 1 + I (k - p)}, E^(4 x)/16])/4^(I (k - p)) - (4^(I (k - p)) cM HypergeometricPFQRegularized[{}, {1 - I k, 1 + I p, 1 - I (k - p)}, E^(4 x)/16])/E^(2 I (k - p) x) + (4^(I (k + p)) cP HypergeometricPFQRegularized[{}, {1 - I k, 1 - I p, 1 - I (k + p)}, E^(4 x)/16])/E^(2 I (k + p) x) - (E^(2 I (k + p) x) cP HypergeometricPFQRegularized[{}, {1 + I k, 1 + I p, 1 + I (k + p)}, E^(4 x)/16])/4^(I (k + p))) /; cP == Csch[k Pi] Csch[(k + p) Pi] Csch[p Pi] && cM == Csch[k Pi] Csch[(k - p) Pi] Csch[p Pi]

 Standard Form

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 MathML Form

 𝒲 y [ ψ k ( y ) ] ( x , p ) - e - i y p ψ _ k ( x - y 2 ) ψ k ( x + y 2 ) d y i 4 π sinh ( π k ) ( c - 4 - i ( k - p ) e 2 i ( k - p ) x 0 F ~ 3 ( 1 + i k , 1 - i p , 1 + i ( k - p ) , e 4 x / 16 ) + c + 4 i ( k + p ) e - 2 i ( k + p ) x 0 F ~ 3 ( 1 - i k , 1 - i p , 1 - i ( k + p ) , e 4 x / 16 ) - c + 4 - i ( k + p ) e 2 i ( k + p ) x 0 F ~ 3 ( 1 + i k , 1 + i p , 1 + i ( k + p ) , e 4 x / 16 ) - c - 4 i ( k - p ) e - 2 i ( k - p ) x 0 F ~ 3 ( 1 - i k , 1 + i p , 1 - i ( k - p ) , e 4 x / 16 ) ) /; c ± csch ( k π ) csch ( p π ) csch ( ( k ± p ) π ) . 𝒲 y [ ψ k ( y ) ] ( x , p ) - e - i y p ψ _ k ( x - y 2 ) ψ k ( x + y 2 ) d y i 4 π sinh ( π k ) ( c - 4 - i ( k - p ) e 2 i ( k - p ) x 0 F ~ 3 ( 1 + i k , 1 - i p , 1 + i ( k - p ) , e 4 x / 16 ) + c + 4 i ( k + p ) e - 2 i ( k + p ) x 0 F ~ 3 ( 1 - i k , 1 - i p , 1 - i ( k + p ) , e 4 x / 16 ) - c + 4 - i ( k + p ) e 2 i ( k + p ) x 0 F ~ 3 ( 1 + i k , 1 + i p , 1 + i ( k + p ) , e 4 x / 16 ) - c - 4 i ( k - p ) e - 2 i ( k - p ) x 0 F ~ 3 ( 1 - i k , 1 + i p , 1 - i ( k - p ) , e 4 x / 16 ) ) /; c ± csch ( k π ) csch ( p π ) csch ( ( k ± p ) π ) . [/itex]

 Rule Form

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

 2001-10-29