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 Cosh

 http://functions.wolfram.com/01.20.21.0451.01

 Input Form

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

 Standard Form

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 MathML Form

 z n cosh ( c z 2 + f z + g ) z - 2 - n - 2 c - n - 1 - f 2 4 c - g ( - f ) n ( f + 2 c z ) ( f 2 2 c j = 0 n ( ( f + 2 c z ) 2 c ) 1 2 ( - j - 1 ) ( - 4 c z f - 2 ) j ( 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 , ( f + 2 c z ) 2 4 c ) + 2 g j = 0 n ( - ( f + 2 c z ) 2 c ) 1 2 ( - j - 1 ) ( - 4 c z f - 2 ) j ( 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 , - ( f + 2 c z ) 2 4 c ) ) /; n Condition z z n c z 2 f z g -1 2 -1 n -2 c -1 n -1 -1 f 2 4 c -1 -1 g -1 f n f 2 c z f 2 2 c -1 j 0 n f 2 c z 2 c -1 1 2 -1 j -1 -1 4 c z f -1 -2 j Binomial n j Gamma j 1 2 -1 f 2 c z 2 4 c -1 2 g j 0 n -1 f 2 c z 2 c -1 1 2 -1 j -1 -1 4 c z f -1 -2 j Binomial n j Gamma j 1 2 -1 -1 f 2 c z 2 4 c -1 n [/itex]

 Rule Form

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

 2002-12-18