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/01.20.21.4900.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18