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 Cosh

 http://functions.wolfram.com/01.20.21.0886.01

 Input Form

 Integrate[z^n Sin[b z^2] Cosh[c z], z] == (-(1/8)) I ((((-I) b)^(-1 - n) Sum[2^(j - n) c^(-j + n) (-c - 2 I b z)^(1 + j) (-((I (-c - 2 I b z)^2)/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (-c - 2 I b z)^2)/(4 b))], {j, 0, n}])/E^((I c^2)/(4 b)) + (((-I) b)^(-1 - n) Sum[2^(j - n) (-c)^(-j + n) (c - 2 I b z)^(1 + j) (-((I (c - 2 I b z)^2)/b))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I (c - 2 I b z)^2)/(4 b))], {j, 0, n}])/ E^((I c^2)/(4 b)) - (I b)^(-1 - n) E^((I c^2)/(4 b)) Sum[2^(j - n) c^(-j + n) (-c + 2 I b z)^(1 + j) ((I (-c + 2 I b z)^2)/b)^ ((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (-c + 2 I b z)^2)/(4 b)], {j, 0, n}] - (I b)^(-1 - n) E^((I c^2)/(4 b)) Sum[2^(j - n) (-c)^(-j + n) (c + 2 I b z)^(1 + j) ((I (c + 2 I b z)^2)/b)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I (c + 2 I b z)^2)/(4 b)], {j, 0, n}]) /; Element[n, Integers] && n >= 0

 Standard Form

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")"]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "j"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "+", "j"]], "2"], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "z"]]]], ")"]], "2"]]], RowBox[List["4", " ", "b"]]]]], "]"]]]]]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 z n sin ( b z 2 ) cosh ( c z ) z - 1 8 ( - c 2 4 b ( j = 0 n 2 j - n c n - j ( - c - 2 b z ) j + 1 ( - ( - c - 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( - c - 2 b z ) 2 4 b ) ) ( - b ) - n - 1 + - c 2 4 b ( j = 0 n 2 j - n ( - c ) n - j ( c - 2 b z ) j + 1 ( - ( c - 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( c - 2 b z ) 2 4 b ) ) ( - b ) - n - 1 - ( b ) - n - 1 c 2 4 b j = 0 n 2 j - n c n - j ( 2 b z - c ) j + 1 ( ( 2 b z - c ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( 2 b z - c ) 2 4 b ) - ( b ) - n - 1 c 2 4 b j = 0 n 2 j - n ( - c ) n - j ( c + 2 b z ) j + 1 ( ( c + 2 b z ) 2 b ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( c + 2 b z ) 2 4 b ) ) /; n Condition z z n b z 2 c z -1 1 8 -1 c 2 4 b -1 j 0 n 2 j -1 n c n -1 j -1 c -1 2 b z j 1 -1 -1 c -1 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 c -1 2 b z 2 4 b -1 -1 b -1 n -1 -1 c 2 4 b -1 j 0 n 2 j -1 n -1 c n -1 j c -1 2 b z j 1 -1 c -1 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 c -1 2 b z 2 4 b -1 -1 b -1 n -1 -1 b -1 n -1 c 2 4 b -1 j 0 n 2 j -1 n c n -1 j 2 b z -1 c j 1 2 b z -1 c 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 2 b z -1 c 2 4 b -1 -1 b -1 n -1 c 2 4 b -1 j 0 n 2 j -1 n -1 c n -1 j c 2 b z j 1 c 2 b z 2 b -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 c 2 b z 2 4 b -1 n [/itex]

 Rule Form

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

 2002-12-18