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; }

 Cos

 http://functions.wolfram.com/01.07.21.2710.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18