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 Cosh

 http://functions.wolfram.com/01.20.21.1450.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18