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 Cosh

 http://functions.wolfram.com/01.20.21.1000.01

 Input Form

 Integrate[z^n Sin[b z^2 + e]^m Cosh[c z^2 + g], z] == (-(-1)^m) 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) z^(1 + n) Sum[(-1)^k Binomial[m, k] (E^(g - 2 I e k + I e m) ((-c + 2 I b k - I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c + 2 I b k - I b m) z^2] + E^(-g - 2 I e k + I e m) ((c + 2 I b k - I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c + 2 I b k - I b m) z^2] + (-1)^m E^(g + 2 I e k - I e m) ((-c - 2 I b k + I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c - 2 I b k + I b m) z^2] + (-1)^m E^(-g + 2 I e k - I e m) ((c - 2 I b k + I b m) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c - 2 I b k + I b m) z^2]), {k, 0, Floor[(1/2) (-1 + m)]}])/I^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 ( c z 2 + g ) z - ( - 1 ) m 2 - m - 2 z 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]]]]] ( 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 ) - - m 2 - m - 2 z n + 1 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]]]]] ( ( - 1 ) m g + 2 e k - e m Γ ( n + 1 2 , ( - c - 2 b k + b m ) z 2 ) ( ( - c - 2 b k + b m ) z 2 ) 1 2 ( - n - 1 ) + ( - 1 ) m - g + 2 e k - e m ( ( c - 2 b k + b m ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( c - 2 b k + b m ) z 2 ) + g - 2 e k + e m ( ( - c + 2 b k - b m ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - c + 2 b k - b m ) z 2 ) + - g - 2 e k + e m ( ( c + 2 b k - b m ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( c + 2 b k - b m ) z 2 ) ) /; n m + Condition z z n b z 2 e m c z 2 g -1 -1 m 2 -1 m -2 z n 1 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 -1 -1 m 2 -1 m -2 z n 1 k 0 m -1 2 -1 -1 k Binomial m k -1 m g 2 e k -1 e m Gamma n 1 2 -1 -1 c -1 2 b k b m z 2 -1 c -1 2 b k b m z 2 1 2 -1 n -1 -1 m -1 g 2 e k -1 e m c -1 2 b k b m z 2 1 2 -1 n -1 Gamma n 1 2 -1 c -1 2 b k b m z 2 g -1 2 e k e m -1 c 2 b k -1 b m z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 c 2 b k -1 b m z 2 -1 g -1 2 e k e m c 2 b k -1 b m z 2 1 2 -1 n -1 Gamma n 1 2 -1 c 2 b k -1 b m z 2 n m SuperPlus [/itex]

 Rule Form

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

 2002-12-18