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/01.20.21.1090.01

 Input Form

 Integrate[z^n Cos[b z^2 + d z + e] Cosh[c z^2 + f z], z] == (1/8) ((-((-I) b - c)^(-1 - n)) E^((-I) e - ((-I) d - f)^2/(4 ((-I) b - c))) Sum[2^(j - n) (I d + f)^(-j + n) ((-I) d - f + 2 ((-I) b - c) z)^(1 + j) (-(((-I) d - f + 2 ((-I) b - c) z)^2/((-I) b - c)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -(((-I) d - f + 2 ((-I) b - c) z)^2/ (4 ((-I) b - c)))], {j, 0, n}] - (I b - c)^(-1 - n) E^(I e - (I d - f)^2/(4 (I b - c))) Sum[2^(j - n) ((-I) d + f)^(-j + n) (I d - f + 2 (I b - c) z)^(1 + j) (-((I d - f + 2 (I b - c) z)^2/(I b - c)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I d - f + 2 (I b - c) z)^2/ (4 (I b - c)))], {j, 0, n}] - ((-I) b + c)^(-1 - n) E^((-I) e - ((-I) d + f)^2/(4 ((-I) b + c))) Sum[2^(j - n) (I d - f)^(-j + n) ((-I) d + f + 2 ((-I) b + c) z)^(1 + j) (-(((-I) d + f + 2 ((-I) b + c) z)^2/((-I) b + c)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -(((-I) d + f + 2 ((-I) b + c) z)^2/ (4 ((-I) b + c)))], {j, 0, n}] - (I b + c)^(-1 - n) E^(I e - (I d + f)^2/(4 (I b + c))) Sum[2^(j - n) ((-I) d - f)^(-j + n) (I d + f + 2 (I b + c) z)^(1 + j) (-((I d + f + 2 (I b + c) z)^2/(I b + c)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I d + f + 2 (I b + c) z)^2/ (4 (I b + c)))], {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 2 + f z ) z 1 8 ( - ( - c - b ) - n - 1 - ( - f + - d ) 2 4 ( - c + - b ) - e j = 0 n 2 j - n ( f + d ) n - j ( - f - d + 2 ( - c + - b ) z ) j + 1 ( - ( - f - d + 2 ( - c + - b ) z ) 2 - c - b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( j + 1 2 , - ( - f - d + 2 ( - c + - b ) z ) 2 4 ( - c - b ) ) - ( b - c ) - n - 1 e - ( d - f ) 2 4 ( b - c ) j = 0 n 2 j - n ( f - d ) n - j ( - f + d + 2 ( b - c ) z ) j + 1 ( - ( - f + d + 2 ( b - c ) z ) 2 b - c ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( j + 1 2 , - ( - f + d + 2 ( b - c ) z ) 2 4 ( b - c ) ) - ( c - b ) - n - 1 - ( f - d ) 2 4 ( c - b ) - e j = 0 n 2 j - n ( d - f ) n - j ( f - d + 2 ( c - b ) z ) j + 1 ( - ( f - d + 2 ( c - b ) z ) 2 c - b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( j + 1 2 , - ( f - d + 2 ( c - b ) z ) 2 4 ( c - b ) ) - ( c + b ) - n - 1 e - ( f + d ) 2 4 ( c + b ) j = 0 n 2 j - n ( - f - d ) n - j ( f + d + 2 ( c + b ) z ) j + 1 ( - ( f + d + 2 ( c + b ) z ) 2 c + b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity, Rule[Editable, True]]], List[TagBox["j", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] Γ ( j + 1 2 , - ( f + d + 2 ( c + b ) z ) 2 4 ( c + b ) ) ) /; n Condition z z n b z 2 d z e c z 2 f z 1 8 -1 -1 c -1 b -1 n -1 -1 -1 f -1 d 2 4 -1 c -1 b -1 -1 e j 0 n 2 j -1 n f d n -1 j -1 f -1 d 2 -1 c -1 b z j 1 -1 -1 f -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 f -1 d 2 -1 c -1 b z 2 4 -1 c -1 b -1 -1 b -1 c -1 n -1 e -1 d -1 f 2 4 b -1 c -1 j 0 n 2 j -1 n f -1 d n -1 j -1 f d 2 b -1 c z j 1 -1 -1 f 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 -1 f d 2 b -1 c z 2 4 b -1 c -1 -1 c -1 b -1 n -1 -1 f -1 d 2 4 c -1 b -1 -1 e j 0 n 2 j -1 n d -1 f n -1 j f -1 d 2 c -1 b z j 1 -1 f -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 f -1 d 2 c -1 b z 2 4 c -1 b -1 -1 c b -1 n -1 e -1 f d 2 4 c b -1 j 0 n 2 j -1 n -1 f -1 d n -1 j f d 2 c b z j 1 -1 f d 2 c b z 2 c b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f 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