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/01.20.21.4901.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18