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 Cosh

 http://functions.wolfram.com/01.20.21.0114.01

 Input Form

 Integrate[z^(2 n - 1) Cosh[a z^2 + b], z] == (-(1/4)) ((E^b (((-1)^(-1 + n) ExpIntegralEi[a z^2])/(-n)! + E^(a z^2) Sum[((-a) z^2)^k/Pochhammer[n, 1 + k - n], {k, 0, -1 + n}] - E^(a z^2) Sum[((-a) z^2)^k/Pochhammer[n, 1 + k - n], {k, n, -1}]))/ (-a)^n + (((-1)^(-1 + n) ExpIntegralEi[(-a) z^2])/(-n)! + Sum[(a z^2)^k/Pochhammer[n, 1 + k - n], {k, 0, -1 + n}]/E^(a z^2) - Sum[(a z^2)^k/Pochhammer[n, 1 + k - n], {k, n, -1}]/E^(a z^2))/ (a^n E^b)) /; Element[n, Integers]

 Standard Form

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 MathML Form

 z 2 n - 1 cosh ( a z 2 + b ) z - 1 4 ( b ( ( - 1 ) n - 1 Ei ( a z 2 ) ( - n ) ! + a z 2 k = 0 n - 1 ( - a z 2 ) k ( n ) k - n + 1 TagBox[SubscriptBox[RowBox[List["(", "n", ")"]], RowBox[List["k", "-", "n", "+", "1"]]], Pochhammer] - a z 2 k = n - 1 ( - a z 2 ) k ( n ) k - n + 1 TagBox[SubscriptBox[RowBox[List["(", "n", ")"]], RowBox[List["k", "-", "n", "+", "1"]]], Pochhammer] ) ( - a ) - n + a - n - b ( ( - 1 ) n - 1 Ei ( - a z 2 ) ( - n ) ! + - a z 2 k = 0 n - 1 ( a z 2 ) k ( n ) k - n + 1 TagBox[SubscriptBox[RowBox[List["(", "n", ")"]], RowBox[List["k", "-", "n", "+", "1"]]], Pochhammer] - - a z 2 k = n - 1 ( a z 2 ) k ( n ) k - n + 1 TagBox[SubscriptBox[RowBox[List["(", "n", ")"]], RowBox[List["k", "-", "n", "+", "1"]]], Pochhammer] ) ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition z z 2 n -1 a z 2 b -1 1 4 b -1 n -1 ExpIntegralEi a z 2 -1 n -1 a z 2 k 0 n -1 -1 a z 2 k Pochhammer n k -1 n 1 -1 -1 a z 2 k n -1 -1 a z 2 k Pochhammer n k -1 n 1 -1 -1 a -1 n a -1 n -1 b -1 n -1 ExpIntegralEi -1 a z 2 -1 n -1 -1 a z 2 k 0 n -1 a z 2 k Pochhammer n k -1 n 1 -1 -1 -1 a z 2 k n -1 a z 2 k Pochhammer n k -1 n 1 -1 n [/itex]

 Rule Form

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

 2002-12-18