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 Cosh

 http://functions.wolfram.com/01.20.21.1151.01

 Input Form

 Integrate[z^n Cos[b Sqrt[z] + e]^m Cosh[c Sqrt[z] + g], z] == ((-2^(-m)) Binomial[m, m/2] (E^g Gamma[2 (1 + n), (-c) Sqrt[z]] + Gamma[2 (1 + n), c Sqrt[z]]/E^g) (1 - Mod[m, 2]))/c^(2 (1 + n)) - Sum[Binomial[m, k] ((E^(g - 2 I e k + I e m) Gamma[2 (1 + n), (-c + 2 I b k - I b m) Sqrt[z]])/(-c + 2 I b k - I b m)^ (2 (1 + n)) + (E^(-g - 2 I e k + I e m) Gamma[2 (1 + n), (c + 2 I b k - I b m) Sqrt[z]])/(c + 2 I b k - I b m)^(2 (1 + n)) + (E^(g + 2 I e k - I e m) Gamma[2 (1 + n), (-c - 2 I b k + I b m) Sqrt[z]])/(-c - 2 I b k + I b m)^(2 (1 + n)) + (E^(-g + 2 I e k - I e m) Gamma[2 (1 + n), (c - 2 I b k + I b m) Sqrt[z]])/(c - 2 I b k + I b m)^(2 (1 + n))), {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18