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/01.20.21.1340.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18