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/01.20.21.1341.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18