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/01.20.21.1372.01

 Input Form

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

 Standard Form

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 MathML Form

 z n b z 2 + d z + e sin ( a z 2 + p z + q ) cosh ( c z 2 + f z + g ) z - 1 8 ( ( b - c - a ) - n - 1 - ( d - f - p ) 2 4 ( b - c - a ) + e - g - q + π 2 j = 0 n 2 j - n ( - d + f + p ) n - j ( d - f - p + 2 ( b - c - a ) z ) j + 1 ( - ( d - f - p + 2 ( b - c - a ) z ) 2 b - c - a ) 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 - f - p + 2 ( b - c - a ) z ) 2 4 ( b - c - a ) ) + ( b - c + a ) - n - 1 - ( d - f + p ) 2 4 ( b - c + a ) + e - g + q - π 2 j = 0 n 2 j - n ( - d + f - p ) n - j ( d - f + p + 2 ( b - c + a ) z ) j + 1 ( - ( d - f + p + 2 ( b - c + a ) z ) 2 b - c + a ) 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 - f + p + 2 ( b - c + a ) z ) 2 4 ( b - c + a ) ) + ( b + c - a ) - n - 1 - ( d + f - p ) 2 4 ( b + c - a ) + e + g - q + π 2 j = 0 n 2 j - n ( - d - f + p ) n - j ( d + f - p + 2 ( b + c - a ) z ) j + 1 ( - ( d + f - p + 2 ( b + c - a ) z ) 2 b + c - a ) 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 + f - p + 2 ( b + c - a ) z ) 2 4 ( b + c - a ) ) + ( b + c + a ) - n - 1 - ( d + f + p ) 2 4 ( b + c + a ) + e + g + q - π 2 j = 0 n 2 j - n ( - d - f - p ) n - j ( d + f + p + 2 ( b + c + a ) z ) j + 1 ( - ( d + f + p + 2 ( b + c + a ) z ) 2 b + c + a ) 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 + f + p + 2 ( b + c + a ) z ) 2 4 ( b + c + a ) ) ) /; n Condition z z n b z 2 d z e a z 2 p z q c z 2 f z g -1 1 8 b -1 c -1 a -1 n -1 -1 d -1 f -1 p 2 4 b -1 c -1 a -1 e -1 g -1 q 2 -1 j 0 n 2 j -1 n -1 d f p n -1 j d -1 f -1 p 2 b -1 c -1 a z j 1 -1 d -1 f -1 p 2 b -1 c -1 a z 2 b -1 c -1 a -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d -1 f -1 p 2 b -1 c -1 a z 2 4 b -1 c -1 a -1 b -1 c a -1 n -1 -1 d -1 f p 2 4 b -1 c a -1 e -1 g q -1 2 -1 j 0 n 2 j -1 n -1 d f -1 p n -1 j d -1 f p 2 b -1 c a z j 1 -1 d -1 f p 2 b -1 c a z 2 b -1 c a -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d -1 f p 2 b -1 c a z 2 4 b -1 c a -1 b c -1 a -1 n -1 -1 d f -1 p 2 4 b c -1 a -1 e g -1 q 2 -1 j 0 n 2 j -1 n -1 d -1 f p n -1 j d f -1 p 2 b c -1 a z j 1 -1 d f -1 p 2 b c -1 a z 2 b c -1 a -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f -1 p 2 b c -1 a z 2 4 b c -1 a -1 b c a -1 n -1 -1 d f p 2 4 b c a -1 e g q -1 2 -1 j 0 n 2 j -1 n -1 d -1 f -1 p n -1 j d f p 2 b c a z j 1 -1 d f p 2 b c a z 2 b c a -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d f p 2 b c a z 2 4 b c a -1 n [/itex]

 Rule Form

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

 2002-12-18