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; }

 Cosh

 http://functions.wolfram.com/01.20.21.4791.01

 Input Form

 Integrate[Sin[d z] (a + b Sinh[e z]^2 + c Cosh[e z]^2)^\[Beta], z] == (-(1/2)) I ((1/(I d + 2 e \[Beta])) ((((4 a E^(2 e z) + b (-1 + E^(2 e z))^2 + c (1 + E^(2 e z))^2)/ E^(2 e z))^\[Beta] AppellF1[-((I d)/(2 e)) - \[Beta], -\[Beta], -\[Beta], 1 - (I d)/(2 e) - \[Beta], ((b + c) E^(2 e z))/ (-2 a + b - c - 2 Sqrt[(a - b) (a + c)]), ((b + c) E^(2 e z))/ (-2 a + b - c + 2 Sqrt[(a - b) (a + c)])])/(4^\[Beta] E^(I d z) (1 - ((b + c) E^(2 e z))/(-2 a + b - c + 2 Sqrt[(a - b) (a + c)]))^ \[Beta] (1 + ((b + c) E^(2 e z))/(2 a - b + c + 2 Sqrt[(a - b) (a + c)]))^\[Beta])) - (1/((-I) d + 2 e \[Beta])) ((E^(I d z) ((4 a E^(2 e z) + b (-1 + E^(2 e z))^2 + c (1 + E^(2 e z))^2)/ E^(2 e z))^\[Beta] AppellF1[(I d)/(2 e) - \[Beta], -\[Beta], -\[Beta], 1 + (I d)/(2 e) - \[Beta], ((b + c) E^(2 e z))/ (-2 a + b - c - 2 Sqrt[(a - b) (a + c)]), ((b + c) E^(2 e z))/ (-2 a + b - c + 2 Sqrt[(a - b) (a + c)])])/ (4^\[Beta] (1 - ((b + c) E^(2 e z))/(-2 a + b - c + 2 Sqrt[(a - b) (a + c)]))^\[Beta] (1 + ((b + c) E^(2 e z))/(2 a - b + c + 2 Sqrt[(a - b) (a + c)]))^ \[Beta])))

 Standard Form

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 MathML Form

 sin ( d z ) ( a + b sinh 2 ( e z ) + c cosh 2 ( e z ) ) β z - 1 2 ( 1 d + 2 e β ( 4 - β - d z ( 1 - ( b + c ) 2 e z - 2 a + b - c + 2 ( a - b ) ( a + c ) ) - β ( 2 e z ( b + c ) 2 a - b + c + 2 ( a - b ) ( a + c ) + 1 ) - β ( - 2 e z ( b ( - 1 + 2 e z ) 2 + 4 a 2 e z + c ( 1 + 2 e z ) 2 ) ) β F 1 AppellF1 ( - d 2 e - β ; - β , - β ; 1 - d 2 e - β ; ( b + c ) 2 e z - 2 a + b - c - 2 ( a - b ) ( a + c ) , ( b + c ) 2 e z - 2 a + b - c + 2 ( a - b ) ( a + c ) ) ) - 1 - d + 2 e β ( 4 - β d z ( 1 - ( b + c ) 2 e z - 2 a + b - c + 2 ( a - b ) ( a + c ) ) - β ( 2 e z ( b + c ) 2 a - b + c + 2 ( a - b ) ( a + c ) + 1 ) - β ( - 2 e z ( b ( - 1 + 2 e z ) 2 + 4 a 2 e z + c ( 1 + 2 e z ) 2 ) ) β F 1 AppellF1 ( d 2 e - β ; - β , - β ; 1 + d 2 e - β ; ( b + c ) 2 e z - 2 a + b - c - 2 ( a - b ) ( a + c ) , ( b + c ) 2 e z - 2 a + b - c + 2 ( a - b ) ( a + c ) ) ) ) z d z a b e z 2 c e z 2 β -1 1 2 1 d 2 e β -1 4 -1 β -1 d z 1 -1 b c 2 e z -2 a b -1 c 2 a -1 b a c 1 2 -1 -1 β 2 e z b c 2 a -1 b c 2 a -1 b a c 1 2 -1 1 -1 β -2 e z b -1 2 e z 2 4 a 2 e z c 1 2 e z 2 β AppellF1 -1 d 2 e -1 -1 β -1 β -1 β 1 -1 d 2 e -1 -1 β b c 2 e z -2 a b -1 c -1 2 a -1 b a c 1 2 -1 b c 2 e z -2 a b -1 c 2 a -1 b a c 1 2 -1 -1 1 -1 d 2 e β -1 4 -1 β d z 1 -1 b c 2 e z -2 a b -1 c 2 a -1 b a c 1 2 -1 -1 β 2 e z b c 2 a -1 b c 2 a -1 b a c 1 2 -1 1 -1 β -2 e z b -1 2 e z 2 4 a 2 e z c 1 2 e z 2 β AppellF1 d 2 e -1 -1 β -1 β -1 β 1 d 2 e -1 -1 β b c 2 e z -2 a b -1 c -1 2 a -1 b a c 1 2 -1 b c 2 e z -2 a b -1 c 2 a -1 b a c 1 2 -1 [/itex]

 Rule Form

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

 2002-12-18