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http://functions.wolfram.com/01.20.21.1221.01
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Integrate[E^(p z) Sin[b z]^m Cosh[c z^2], z] ==
-((1/c) (2^(-2 - m) Sqrt[Pi] Binomial[m, m/2]
(Sqrt[-c] E^(p^2/(4 c)) Erfi[(p - 2 c z)/(2 Sqrt[-c])] -
(Sqrt[c] Erfi[(p + 2 c z)/(2 Sqrt[c])])/E^(p^2/(4 c)))
(1 - Mod[m, 2]))) - (1/c) (2^(-2 - m) Sqrt[Pi]
Sum[(-1)^k Binomial[m, k]
(Sqrt[-c] E^((((-I) b (2 k - m) + p)^2 - 2 I c m Pi)/(4 c))
Erfi[((-I) b (2 k - m) + p - 2 c z)/(2 Sqrt[-c])] +
Sqrt[-c] E^((((-I) b (-2 k + m) + p)^2 + 2 I c m Pi)/(4 c))
Erfi[((-I) b (-2 k + m) + p - 2 c z)/(2 Sqrt[-c])] -
(Sqrt[c] Erfi[(I b (2 k - m) + p + 2 c z)/(2 Sqrt[c])])/
E^(((I b (2 k - m) + p)^2 - 2 I c m Pi)/(4 c)) -
(Sqrt[c] Erfi[(I b (-2 k + m) + p + 2 c z)/(2 Sqrt[c])])/
E^(((I b (-2 k + m) + p)^2 + 2 I c m Pi)/(4 c))),
{k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0
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<cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <imaginaryi /> <ci> c </ci> <ci> m </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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