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/01.20.21.0914.01

 Input Form

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

 Standard Form

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 MathML Form

 z n sin ( b z 2 + d z + e ) cosh ( c z 2 ) z - 1 8 ( 1 4 ( - d 2 c - b - 4 e ) ( j = 0 n 2 j - n ( d ) n - j ( - d + 2 ( - c - b ) z ) j + 1 ( - ( - d + 2 ( - c - b ) z ) 2 - c - 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 , - ( - d + 2 ( - c - b ) z ) 2 4 ( - c - b ) ) ) ( - c - b ) - n - 1 - ( b - c ) - n - 1 1 4 ( d 2 - b - c + 4 e ) j = 0 n 2 j - n ( - d ) n - j ( d + 2 ( b - c ) z ) j + 1 ( - ( d + 2 ( b - c ) z ) 2 b - c ) 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 , - ( d + 2 ( b - c ) z ) 2 4 ( b - c ) ) + ( c - b ) - n - 1 - 1 4 ( d 2 - b - c + 4 e ) j = 0 n 2 j - n ( d ) n - j ( - d + 2 ( c - b ) z ) j + 1 ( - ( - d + 2 ( c - b ) z ) 2 c - 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 , - ( - d + 2 ( c - b ) z ) 2 4 ( c - b ) ) - ( c + b ) - n - 1 - 1 4 ( - d 2 c - b - 4 e ) j = 0 n 2 j - n ( - d ) n - j ( d + 2 ( c + b ) z ) j + 1 ( - ( d + 2 ( c + b ) z ) 2 c + 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 , - ( d + 2 ( c + b ) z ) 2 4 ( c + b ) ) ) /; n Condition z z n b z 2 d z e c z 2 -1 1 8 1 4 -1 d 2 c -1 b -1 -1 4 e j 0 n 2 j -1 n d n -1 j -1 d 2 -1 c -1 b z j 1 -1 -1 d 2 -1 c -1 b z 2 -1 c -1 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 d 2 -1 c -1 b z 2 4 -1 c -1 b -1 -1 c -1 b -1 n -1 -1 b -1 c -1 n -1 1 4 d 2 -1 b -1 c -1 4 e j 0 n 2 j -1 n -1 d n -1 j d 2 b -1 c z j 1 -1 d 2 b -1 c z 2 b -1 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 b -1 c z 2 4 b -1 c -1 c -1 b -1 n -1 -1 1 4 d 2 -1 b -1 c -1 4 e j 0 n 2 j -1 n d n -1 j -1 d 2 c -1 b z j 1 -1 -1 d 2 c -1 b z 2 c -1 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 d 2 c -1 b z 2 4 c -1 b -1 -1 c b -1 n -1 -1 1 4 -1 d 2 c -1 b -1 -1 4 e j 0 n 2 j -1 n -1 d n -1 j d 2 c b z j 1 -1 d 2 c b z 2 c b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 c b z 2 4 c b -1 n [/itex]

 Rule Form

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

 2002-12-18