html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.0960.01

 Input Form

 Integrate[z^(\[Alpha] - 1) Sin[d + c z]^m Cosh[b + a z], z] == 2^(-1 - m) z^\[Alpha] ((Binomial[m, m/2] (-1 + Mod[m, 2]) (((-a) z)^\[Alpha] Gamma[\[Alpha], a z] Exp[-b] + (a z)^\[Alpha] Gamma[\[Alpha], (-a) z] Exp[b]))/ (((-a) z)^\[Alpha] (a z)^\[Alpha]) - Sum[((-1)^k Binomial[m, k] (((-a - I c (2 k - m)) z)^\[Alpha] ((a + I c (2 k - m)) z)^\[Alpha] ((-a + 2 I c k - I c m) z)^\[Alpha] Gamma[\[Alpha], (a + I c (-2 k + m)) z] E^(-b + (1/2) I (4 d k - 2 d m + m Pi)) + ((a + I c (-2 k + m)) z)^\[Alpha] ((((-a - I c (2 k - m)) z)^\[Alpha] ((((-a + 2 I c k - I c m) z)^\[Alpha] Gamma[\[Alpha], (a + 2 I c k - I c m) z])/E^b + ((a + 2 I c k - I c m) z)^ \[Alpha] Gamma[\[Alpha], (-a + 2 I c k - I c m) z] E^b))/ E^((1/2) I (4 d k - 2 d m + m Pi)) + ((a + I c (2 k - m)) z)^ \[Alpha] ((-a + 2 I c k - I c m) z)^\[Alpha] Gamma[\[Alpha], (-a - I c (2 k - m)) z] E^(b + (1/2) I (4 d k - 2 d m + m Pi)))))/ (((-a - I c (2 k - m)) z)^\[Alpha] ((a + I c (2 k - m)) z)^\[Alpha] ((-a + 2 I c k - I c m) z)^\[Alpha] ((a + I c (-2 k + m)) z)^ \[Alpha]), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z α - 1 sin m ( d + c z ) cosh ( b + a z ) z 2 - m - 1 z α ( ( - a z ) - α ( a z ) - α ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( m mod 2 \$CellContext`m 2 - 1 ) ( - b Γ ( α , a z ) ( - a z ) α + ( a z ) α b Γ ( α , - a z ) ) - k = 0 m - 1 2 ( - 1 ) k ( ( - a - c ( 2 k - m ) ) z ) - α ( ( a + c ( 2 k - m ) ) z ) - α ( ( - a + 2 c k - c m ) z ) - α ( ( a + c ( m - 2 k ) ) z ) - α ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 2 ( 4 d k - 2 d m + m π ) - b ( ( a + c ( 2 k - m ) ) z ) α ( ( - a - c ( 2 k - m ) ) z ) α Γ ( α , ( a + c ( m - 2 k ) ) z ) ( ( - a + 2 c k - c m ) z ) α + ( - 1 2 ( 4 d k - 2 d m + m π ) ( - b Γ ( α , ( a + 2 c k - c m ) z ) ( ( - a + 2 c k - c m ) z ) α + b ( ( a + 2 c k - c m ) z ) α Γ ( α , ( - a + 2 c k - c m ) z ) ) ( ( - a - c ( 2 k - m ) ) z ) α + b + 1 2 ( 4 d k - 2 d m + m π ) ( ( a + c ( 2 k - m ) ) z ) α ( ( - a + 2 c k - c m ) z ) α Γ ( α , ( - a - c ( 2 k - m ) ) z ) ) ( ( a + c ( m - 2 k ) ) z ) α ) ) /; m + Condition z z α -1 d c z m b a z 2 -1 m -1 z α -1 a z -1 α a z -1 α Binomial m m 2 -1 \$CellContext`m 2 -1 -1 b Gamma α a z -1 a z α a z α b Gamma α -1 a z -1 k 0 m -1 2 -1 -1 k -1 a -1 c 2 k -1 m z -1 α a c 2 k -1 m z -1 α -1 a 2 c k -1 c m z -1 α a c m -1 2 k z -1 α Binomial m k 1 2 4 d k -1 2 d m m -1 b a c 2 k -1 m z α -1 a -1 c 2 k -1 m z α Gamma α a c m -1 2 k z -1 a 2 c k -1 c m z α -1 1 2 4 d k -1 2 d m m -1 b Gamma α a 2 c k -1 c m z -1 a 2 c k -1 c m z α b a 2 c k -1 c m z α Gamma α -1 a 2 c k -1 c m z -1 a -1 c 2 k -1 m z α b 1 2 4 d k -1 2 d m m a c 2 k -1 m z α -1 a 2 c k -1 c m z α Gamma α -1 a -1 c 2 k -1 m z a c m -1 2 k z α m SuperPlus [/itex]

 Rule Form

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

 2002-12-18