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 Cosh

 http://functions.wolfram.com/01.20.21.1395.01

 Input Form

 Integrate[z^n E^(p z^2) Sin[b z^2]^m Cosh[c z^2], z] == (-2^(-2 - m)) z^(1 + n) Binomial[m, m/2] (((-c - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c - p) z^2] + ((c - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c - p) z^2]) (1 - Mod[m, 2]) - 2^(-2 - m) z^(1 + n) Sum[(-1)^k Binomial[m, k] ((((-c - I b (-2 k + m) - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c - I b (-2 k + m) - p) z^2])/E^((1/2) I m Pi) + (((c - I b (-2 k + m) - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c - I b (-2 k + m) - p) z^2])/E^((1/2) I m Pi) + E^((I m Pi)/2) ((-c + I b (-2 k + m) - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-c + I b (-2 k + m) - p) z^2] + E^((I m Pi)/2) ((c + I b (-2 k + m) - p) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (c + I b (-2 k + m) - p) 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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"p"]], ")"]], " ", 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 p z 2 sin m ( b z 2 ) cosh ( c z 2 ) 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]]]]] ( Γ ( n + 1 2 , ( - c - p ) z 2 ) ( ( - c - p ) z 2 ) 1 2 ( - n - 1 ) + ( ( c - p ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( c - p ) 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]]]]] ( m π 2 Γ ( n + 1 2 , ( - c + b ( m - 2 k ) - p ) z 2 ) ( ( - c + b ( m - 2 k ) - p ) z 2 ) 1 2 ( - n - 1 ) + m π 2 ( ( c + b ( m - 2 k ) - p ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( c + b ( m - 2 k ) - p ) z 2 ) + - 1 2 m π ( ( - c - b ( m - 2 k ) - p ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( - c - b ( m - 2 k ) - p ) z 2 ) + - 1 2 m π ( ( c - b ( m - 2 k ) - p ) z 2 ) 1 2 ( - n - 1 ) Γ ( n + 1 2 , ( c - b ( m - 2 k ) - p ) z 2 ) ) ) z n + 1 /; m + n Condition z z n p z 2 b z 2 m c z 2 -1 2 -1 m -2 Binomial m m 2 -1 Gamma n 1 2 -1 -1 c -1 p z 2 -1 c -1 p z 2 1 2 -1 n -1 c -1 p z 2 1 2 -1 n -1 Gamma n 1 2 -1 c -1 p 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 m 2 -1 Gamma n 1 2 -1 -1 c b m -1 2 k -1 p z 2 -1 c b m -1 2 k -1 p z 2 1 2 -1 n -1 m 2 -1 c b m -1 2 k -1 p z 2 1 2 -1 n -1 Gamma n 1 2 -1 c b m -1 2 k -1 p z 2 -1 1 2 m -1 c -1 b m -1 2 k -1 p z 2 1 2 -1 n -1 Gamma n 1 2 -1 -1 c -1 b m -1 2 k -1 p z 2 -1 1 2 m c -1 b m -1 2 k -1 p z 2 1 2 -1 n -1 Gamma n 1 2 -1 c -1 b m -1 2 k -1 p 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