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http://functions.wolfram.com/01.20.21.3764.01
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Integrate[E^(p z) Sin[c z]^\[Mu] Cosh[b + a z]^v, z] ==
(1/(p - I c \[Mu])) ((E^(p z) Binomial[v, v/2] Hypergeometric2F1[
-((I (p - I c \[Mu]))/(2 c)), -\[Mu], (1/2) (2 - (I p)/c - \[Mu]),
E^(2 I c z)] (1 - Mod[v, 2]) Sin[c z]^\[Mu])/
(2^v (1 - E^(2 I c z))^\[Mu])) +
(Sin[c z]^\[Mu] Sum[E^(b (-2 k + v)) Binomial[v, k]
((E^(-2 b (-2 k + v) + (p - a (-2 k + v)) z) Hypergeometric2F1[
-((I (p - a (-2 k + v) - I c \[Mu]))/(2 c)), -\[Mu],
(1/2) (2 - (I (p - a (-2 k + v)))/c - \[Mu]), E^(2 I c z)])/
(p - a (-2 k + v) - I c \[Mu]) + (E^((p + a (-2 k + v)) z)
Hypergeometric2F1[-((I (p + a (-2 k + v) - I c \[Mu]))/(2 c)),
-\[Mu], (1/2) (2 - (I (p + a (-2 k + v)))/c - \[Mu]),
E^(2 I c z)])/(p + a (-2 k + v) - I c \[Mu])),
{k, 0, Floor[(1/2) (-1 + v)]}])/(2^v (1 - E^(2 I c z))^\[Mu]) /;
Element[v, Integers] && v > 0
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</mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> μ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> </mrow> <mo> ; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> c </mi> </mfrac> </mrow> <mo> - </mo> <mi> μ </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ; </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> 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Date Added to functions.wolfram.com (modification date)
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