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/01.20.21.3878.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18