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http://functions.wolfram.com/01.07.21.2620.01
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Integrate[E^(p z) Sin[d + c z]^\[Mu] Cos[b + a z]^v, z] ==
(-((1/(p - I c \[Mu])) ((E^(p z) Binomial[v, v/2] Hypergeometric2F1[
-((I p + c \[Mu])/(2 c)), -\[Mu], (1/2) (2 - (I p)/c - \[Mu]),
E^(2 I (d + c z))] (-1 + Mod[v, 2]) Sin[d + c z]^\[Mu])/
(1 - E^(2 (I d + I c z)))^\[Mu])) +
(Sin[d + c z]^\[Mu] Sum[E^(2 I b s - I b v) Binomial[v, s]
((E^((p + 2 I a s - I a v) z) Hypergeometric2F1[
-((I (p + 2 I a s - I a v - I c \[Mu]))/(2 c)), -\[Mu],
-((I (p + 2 I a s - I a v - I c (-2 + \[Mu])))/(2 c)),
E^(2 I (d + c z))])/(p + 2 I a s - I a v - I c \[Mu]) +
(E^(2 I b (-2 s + v) + (p + I a (-2 s + v)) z) Hypergeometric2F1[
-((I (p - 2 I a s + I a v - I c \[Mu]))/(2 c)), -\[Mu],
(1/2) (2 - (I (p - 2 I a s + I a v))/c - \[Mu]),
E^(2 I (d + c z))])/(p - 2 I a s + I a v - I c \[Mu])),
{s, 0, Floor[(1/2) (-1 + v)]}])/(1 - E^(2 (I d + I c z)))^\[Mu])/
2^v /; Element[v, Integers] && v > 0
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</apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> μ </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> </apply> <apply> <ci> Binomial </ci> <ci> v </ci> <apply> <times /> <ci> v </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <ci> c </ci> <ci> μ </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> p </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> μ </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <plus /> <ci> d </ci> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <sin /> <apply> <plus /> <ci> d </ci> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <ci> μ </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> v </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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