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/01.20.21.0972.01

 Input Form

 Integrate[z^n Sin[b z^2 + e]^m Cosh[f z + g], z] == 2^(-1 - m) f^(-1 - n) Binomial[m, m/2] ((-1)^n E^g Gamma[1 + n, (-f) z] - Gamma[1 + n, f z]/E^g) (1 - Mod[m, 2]) - 2^(-2 - m) Sum[(-1)^s Binomial[m, s] (E^(-g + (I m Pi)/2 - (I f^2)/(4 b (m - 2 s)) - I e (m - 2 s)) ((-I) b (m - 2 s))^(-1 - n) Sum[2^(j - n) f^(-j + n) (-f - 2 I b (m - 2 s) z)^(1 + j) (-((I (-f - 2 I b (m - 2 s) z)^2)/ (b (m - 2 s))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (-f - 2 I b (m - 2 s) z)^2)/ (4 b (m - 2 s)))], {j, 0, n}] + E^(g + (I m Pi)/2 - (I f^2)/(4 b (m - 2 s)) - I e (m - 2 s)) ((-I) b (m - 2 s))^(-1 - n) Sum[2^(j - n) (-f)^(-j + n) (f - 2 I b (m - 2 s) z)^(1 + j) (-((I (f - 2 I b (m - 2 s) z)^2)/ (b (m - 2 s))))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (f - 2 I b (m - 2 s) z)^2)/(4 b (m - 2 s)))], {j, 0, n}] + E^(-g - (I m Pi)/2 + (I f^2)/(4 b (m - 2 s)) + I e (m - 2 s)) (I b (m - 2 s))^(-1 - n) Sum[2^(j - n) f^(-j + n) (-f + 2 I b (m - 2 s) z)^(1 + j) ((I (-f + 2 I b (m - 2 s) z)^2)/(b (m - 2 s)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (-f + 2 I b (m - 2 s) z)^2)/ (4 b (m - 2 s))], {j, 0, n}] + E^(g - (I m Pi)/2 + (I f^2)/(4 b (m - 2 s)) + I e (m - 2 s)) (I b (m - 2 s))^(-1 - n) Sum[2^(j - n) (-f)^(-j + n) (f + 2 I b (m - 2 s) z)^(1 + j) ((I (f + 2 I b (m - 2 s) z)^2)/ (b (m - 2 s)))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (f + 2 I b (m - 2 s) z)^2)/(4 b (m - 2 s))], {j, 0, n}]), {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z n sin m ( b z 2 + e ) cosh ( g + f z ) z 2 - m - 1 f - n - 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - 1 ) n g Γ ( n + 1 , - f z ) - - g Γ ( n + 1 , f z ) ) ( 1 - m mod 2 \$CellContext`m 2 ) - 2 - m - 2 s = 0 m - 1 2 ( - 1 ) s ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - f 2 4 b ( m - 2 s ) - g - e ( m - 2 s ) + m π 2 ( j = 0 n 2 j - n f n - j ( - f - 2 b ( m - 2 s ) z ) j + 1 ( - ( - f - 2 b ( m - 2 s ) z ) 2 b ( m - 2 s ) ) 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 , - ( - f - 2 b ( m - 2 s ) z ) 2 4 b ( m - 2 s ) ) ) ( - b ( m - 2 s ) ) - n - 1 + - f 2 4 b ( m - 2 s ) + g - e ( m - 2 s ) + m π 2 ( j = 0 n 2 j - n ( - f ) n - j ( f - 2 b ( m - 2 s ) z ) j + 1 ( - ( f - 2 b ( m - 2 s ) z ) 2 b ( m - 2 s ) ) 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 , - ( f - 2 b ( m - 2 s ) z ) 2 4 b ( m - 2 s ) ) ) ( - b ( m - 2 s ) ) - n - 1 + f 2 4 b ( m - 2 s ) - g + e ( m - 2 s ) - m π 2 ( b ( m - 2 s ) ) - n - 1 j = 0 n 2 j - n f n - j ( 2 b ( m - 2 s ) z - f ) j + 1 ( ( 2 b ( m - 2 s ) z - f ) 2 b ( m - 2 s ) ) 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 , ( 2 b ( m - 2 s ) z - f ) 2 4 b ( m - 2 s ) ) + f 2 4 b ( m - 2 s ) + g + e ( m - 2 s ) - m π 2 ( b ( m - 2 s ) ) - n - 1 j = 0 n 2 j - n ( - f ) n - j ( f + 2 b ( m - 2 s ) z ) j + 1 ( ( f + 2 b ( m - 2 s ) z ) 2 b ( m - 2 s ) ) 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 , ( f + 2 b ( m - 2 s ) z ) 2 4 b ( m - 2 s ) ) ) /; n m + Condition z z n b z 2 e m g f z 2 -1 m -1 f -1 n -1 Binomial m m 2 -1 -1 n g Gamma n 1 -1 f z -1 -1 g Gamma n 1 f z 1 -1 \$CellContext`m 2 -1 2 -1 m -2 s 0 m -1 2 -1 -1 s Binomial m s -1 f 2 4 b m -1 2 s -1 -1 g -1 e m -1 2 s m 2 -1 j 0 n 2 j -1 n f n -1 j -1 f -1 2 b m -1 2 s z j 1 -1 -1 f -1 2 b m -1 2 s z 2 b m -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 f -1 2 b m -1 2 s z 2 4 b m -1 2 s -1 -1 b m -1 2 s -1 n -1 -1 f 2 4 b m -1 2 s -1 g -1 e m -1 2 s m 2 -1 j 0 n 2 j -1 n -1 f n -1 j f -1 2 b m -1 2 s z j 1 -1 f -1 2 b m -1 2 s z 2 b m -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f -1 2 b m -1 2 s z 2 4 b m -1 2 s -1 -1 b m -1 2 s -1 n -1 f 2 4 b m -1 2 s -1 -1 g e m -1 2 s -1 m 2 -1 b m -1 2 s -1 n -1 j 0 n 2 j -1 n f n -1 j 2 b m -1 2 s z -1 f j 1 2 b m -1 2 s z -1 f 2 b m -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 2 b m -1 2 s z -1 f 2 4 b m -1 2 s -1 f 2 4 b m -1 2 s -1 g e m -1 2 s -1 m 2 -1 b m -1 2 s -1 n -1 j 0 n 2 j -1 n -1 f n -1 j f 2 b m -1 2 s z j 1 f 2 b m -1 2 s z 2 b m -1 2 s -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 f 2 b m -1 2 s z 2 4 b m -1 2 s -1 n m SuperPlus [/itex]

 Rule Form

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

 2002-12-18