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 Cosh

 http://functions.wolfram.com/01.20.21.1398.01

 Input Form

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

 Standard Form

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")"]], " ", SuperscriptBox["z", "2"]]]]], "]"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n b z 2 + e sin m ( a z 2 + q ) 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]]]]] ( e + g Γ ( n + 1 2 , ( - b - c ) z 2 ) ( ( - b - c ) z 2 ) 1 2 ( - n - 1 ) + e - g ( ( c - b ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( c - b ) 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]]]]] ( e + g - ( m - 2 k ) q + m π 2 Γ ( n + 1 2 , ( - b - c + a ( m - 2 k ) ) z 2 ) ( ( - b - c + a ( m - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) + e - g - ( m - 2 k ) q + m π 2 ( ( - b + c + a ( m - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + c + a ( m - 2 k ) ) z 2 ) + e + g + ( m - 2 k ) q - m π 2 ( ( - b - c - a ( m - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b - c - a ( m - 2 k ) ) z 2 ) + e - g + ( m - 2 k ) q - m π 2 ( ( - b + c - a ( m - 2 k ) ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - b + c - a ( m - 2 k ) ) z 2 ) ) ) z n + 1 /; m + n Condition z z n b z 2 e a z 2 q m c z 2 g -1 2 -1 m -2 Binomial m m 2 -1 e g Gamma n 1 2 -1 -1 b -1 c z 2 -1 b -1 c z 2 1 2 -1 n -1 e -1 g c -1 b z 2 1 2 -1 n -1 Gamma n 1 2 -1 c -1 b 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 e g -1 m -1 2 k q m 2 -1 Gamma n 1 2 -1 -1 b -1 c a m -1 2 k z 2 -1 b -1 c a m -1 2 k z 2 1 2 -1 n -1 e -1 g -1 m -1 2 k q m 2 -1 -1 b c a m -1 2 k z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b c a m -1 2 k z 2 e g m -1 2 k q -1 m 2 -1 -1 b -1 c -1 a m -1 2 k z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b -1 c -1 a m -1 2 k z 2 e -1 g m -1 2 k q -1 m 2 -1 -1 b c -1 a m -1 2 k z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 b c -1 a m -1 2 k z 2 z n 1 m SuperPlus n [/itex]

 Rule Form

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

 2002-12-18