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/01.20.21.0992.01

 Input Form

 Integrate[z^n Sin[d z]^m Cosh[c z^2 + g], z] == (-2^(-2 - m)) z^(1 + n) Binomial[m, m/2] (E^g ((-c) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c) z^2] + ((c z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, c z^2])/E^g) (1 - Mod[m, 2]) - 2^(-2 - m) Sum[(-1)^k Binomial[m, k] ((-c)^(-1 - n) E^(-g - (d^2 (-2 k + m)^2)/(4 c) + (I m Pi)/2) Sum[2^(j - n) (I d (-2 k + m))^(-j + n) ((-I) d (-2 k + m) - 2 c z)^ (1 + j) (((-I) d (-2 k + m) - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, ((-I) d (-2 k + m) - 2 c z)^2/ (4 c)], {j, 0, n}] + (-c)^(-1 - n) E^(-g - (d^2 (-2 k + m)^2)/(4 c) - (I m Pi)/2) Sum[2^(j - n) ((-I) d (-2 k + m))^(-j + n) (I d (-2 k + m) - 2 c z)^ (1 + j) ((I d (-2 k + m) - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I d (-2 k + m) - 2 c z)^2/(4 c)], {j, 0, n}] + c^(-1 - n) E^(g + (d^2 (-2 k + m)^2)/(4 c) + (I m Pi)/2) Sum[2^(j - n) (I d (-2 k + m))^(-j + n) ((-I) d (-2 k + m) + 2 c z)^(1 + j) (-(((-I) d (-2 k + m) + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -(((-I) d (-2 k + m) + 2 c z)^2/ (4 c))], {j, 0, n}] + c^(-1 - n) E^(g + (d^2 (-2 k + m)^2)/(4 c) - (I m Pi)/2) Sum[2^(j - n) ((-I) d (-2 k + m))^(-j + n) (I d (-2 k + m) + 2 c z)^ (1 + j) (-((I d (-2 k + m) + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I d (-2 k + m) + 2 c z)^2/ (4 c))], {j, 0, n}]), {k, 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 ( d z ) cosh ( c z 2 + g ) z - 2 - m - 2 ( 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]]]]] ( g Γ ( n + 1 2 , - c z 2 ) ( - c z 2 ) 1 2 ( - n - 1 ) + - g ( c z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , c z 2 ) ) ( 1 - m mod 2 \$CellContext`m 2 ) z n + 1 - 2 - m - 2 k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - d 2 ( m - 2 k ) 2 4 c - g + m π 2 ( j = 0 n 2 j - n ( d ( m - 2 k ) ) n - j ( - d ( m - 2 k ) - 2 c z ) j + 1 ( ( - d ( m - 2 k ) - 2 c z ) 2 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 ( m - 2 k ) - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 + - d 2 ( m - 2 k ) 2 4 c - g - m π 2 ( j = 0 n 2 j - n ( - d ( m - 2 k ) ) n - j ( d ( m - 2 k ) - 2 c z ) j + 1 ( ( d ( m - 2 k ) - 2 c z ) 2 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 ( m - 2 k ) - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 + c - n - 1 d 2 ( m - 2 k ) 2 4 c + g + m π 2 j = 0 n 2 j - n ( d ( m - 2 k ) ) n - j ( 2 c z - d ( m - 2 k ) ) j + 1 ( - ( 2 c z - d ( m - 2 k ) ) 2 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 , - ( 2 c z - d ( m - 2 k ) ) 2 4 c ) + c - n - 1 d 2 ( m - 2 k ) 2 4 c + g - m π 2 j = 0 n 2 j - n ( - d ( m - 2 k ) ) n - j ( d ( m - 2 k ) + 2 c z ) j + 1 ( - ( d ( m - 2 k ) + 2 c z ) 2 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 ( m - 2 k ) + 2 c z ) 2 4 c ) ) /; n m + Condition z z n d z m c z 2 g -1 2 -1 m -2 Binomial m m 2 -1 g Gamma n 1 2 -1 -1 c z 2 -1 c z 2 1 2 -1 n -1 -1 g c z 2 1 2 -1 n -1 Gamma n 1 2 -1 c z 2 1 -1 \$CellContext`m 2 z n 1 -1 2 -1 m -2 k 0 m -1 2 -1 -1 k Binomial m k -1 d 2 m -1 2 k 2 4 c -1 -1 g m 2 -1 j 0 n 2 j -1 n d m -1 2 k n -1 j -1 d m -1 2 k -1 2 c z j 1 -1 d m -1 2 k -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k -1 2 c z 2 4 c -1 -1 c -1 n -1 -1 d 2 m -1 2 k 2 4 c -1 -1 g -1 m 2 -1 j 0 n 2 j -1 n -1 d m -1 2 k n -1 j d m -1 2 k -1 2 c z j 1 d m -1 2 k -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 d m -1 2 k -1 2 c z 2 4 c -1 -1 c -1 n -1 c -1 n -1 d 2 m -1 2 k 2 4 c -1 g m 2 -1 j 0 n 2 j -1 n d m -1 2 k n -1 j 2 c z -1 d m -1 2 k j 1 -1 2 c z -1 d m -1 2 k 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 2 c z -1 d m -1 2 k 2 4 c -1 c -1 n -1 d 2 m -1 2 k 2 4 c -1 g -1 m 2 -1 j 0 n 2 j -1 n -1 d m -1 2 k n -1 j d m -1 2 k 2 c z j 1 -1 d m -1 2 k 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d m -1 2 k 2 c z 2 4 c -1 n m SuperPlus [/itex]

 Rule Form

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

 2002-12-18