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/01.20.21.1042.01

 Input Form

 Integrate[z^n Cos[b z^2 + d z + e] Cosh[c z], z] == (1/8) ((-((-I) b)^(-1 - n)) E^(-((I (-c - I d)^2)/(4 b)) - I e) Sum[2^(j - n) (c + I d)^(-j + n) (-c - I d - 2 I b z)^(1 + j) (-((I (-c - I d - 2 I b z)^2)/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (-c - I d - 2 I b z)^2)/(4 b))], {j, 0, n}] - ((-I) b)^(-1 - n) E^(-((I (c - I d)^2)/(4 b)) - I e) Sum[2^(j - n) (-c + I d)^(-j + n) (c - I d - 2 I b z)^(1 + j) (-((I (c - I d - 2 I b z)^2)/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (c - I d - 2 I b z)^2)/(4 b))], {j, 0, n}] - (I b)^(-1 - n) E^((I (-c + I d)^2)/(4 b) + I e) Sum[2^(j - n) (c - I d)^(-j + n) (-c + I d + 2 I b z)^(1 + j) ((I (-c + I d + 2 I b z)^2)/b)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (-c + I d + 2 I b z)^2)/(4 b)], {j, 0, n}] - (I b)^(-1 - n) E^((I (c + I d)^2)/(4 b) + I e) Sum[2^(j - n) (-c - I d)^(-j + n) (c + I d + 2 I b z)^(1 + j) ((I (c + I d + 2 I b z)^2)/b)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (c + I d + 2 I b z)^2)/(4 b)], {j, 0, n}]) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n cos ( b z 2 + d z + e ) cosh ( c z ) z 1 8 ( - - ( c - d ) 2 4 b - e ( j = 0 n 2 j - n ( d - c ) n - j ( c - d - 2 b z ) j + 1 ( - ( c - d - 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( c - d - 2 b z ) 2 4 b ) ) ( - b ) - n - 1 - ( b ) - n - 1 ( d - c ) 2 4 b + e j = 0 n 2 j - n ( c - d ) n - j ( - c + d + 2 b z ) j + 1 ( ( - c + d + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( - c + d + 2 b z ) 2 4 b ) - ( b ) - n - 1 ( c + d ) 2 4 b + e j = 0 n 2 j - n ( - c - d ) n - j ( c + d + 2 b z ) j + 1 ( ( c + d + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( c + d + 2 b z ) 2 4 b ) - ( - b ) - n - 1 - ( - c - d ) 2 4 b - e j = 0 n 2 j - n ( c + d ) n - j ( - c - d - 2 b z ) j + 1 ( - ( - c - d - 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( - c - d - 2 b z ) 2 4 b ) ) /; n Condition z z n b z 2 d z e c z 1 8 -1 -1 c -1 d 2 4 b -1 -1 e j 0 n 2 j -1 n d -1 c n -1 j c -1 d -1 2 b z j 1 -1 c -1 d -1 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 c -1 d -1 2 b z 2 4 b -1 -1 b -1 n -1 -1 b -1 n -1 d -1 c 2 4 b -1 e j 0 n 2 j -1 n c -1 d n -1 j -1 c d 2 b z j 1 -1 c d 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 c d 2 b z 2 4 b -1 -1 b -1 n -1 c d 2 4 b -1 e j 0 n 2 j -1 n -1 c -1 d n -1 j c d 2 b z j 1 c d 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 c d 2 b z 2 4 b -1 -1 -1 b -1 n -1 -1 -1 c -1 d 2 4 b -1 -1 e j 0 n 2 j -1 n c d n -1 j -1 c -1 d -1 2 b z j 1 -1 -1 c -1 d -1 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 c -1 d -1 2 b z 2 4 b -1 n [/itex]

 Rule Form

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

 2002-12-18