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/01.20.21.0917.01

 Input Form

 Integrate[z^n Sin[d z] Cosh[c Sqrt[z] + g], z] == (I (-1)^(-1 + n) 2^(-3 - 2 n) (E^(-((I c^2)/(4 d)) - g) Sum[(-1)^(-h + j) 4^j (-c)^(-h - j + 2 n) (-c - 2 I d Sqrt[z])^(h + j) (-((I (-c - 2 I d Sqrt[z])^2)/d))^((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c) (-c - 2 I d Sqrt[z]) Gamma[(1/2) (1 + h + j), -((I (-c - 2 I d Sqrt[z])^2)/(4 d))] - 2 I d Sqrt[-((I (-c - 2 I d Sqrt[z])^2)/d)] Gamma[(1/2) (2 + h + j), -((I (-c - 2 I d Sqrt[z])^2)/(4 d))]), {j, 0, n}, {h, 0, j}] + E^(-((I c^2)/(4 d)) + g) Sum[(-1)^(-h + j) 4^j c^(-h - j + 2 n) (c - 2 I d Sqrt[z])^(h + j) (-((I (c - 2 I d Sqrt[z])^2)/d))^ ((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] (c (c - 2 I d Sqrt[z]) Gamma[(1/2) (1 + h + j), -((I (c - 2 I d Sqrt[z])^2)/(4 d))] - 2 I d Sqrt[-((I (c - 2 I d Sqrt[z])^2)/d)] Gamma[(1/2) (2 + h + j), -((I (c - 2 I d Sqrt[z])^2)/(4 d))]), {j, 0, n}, {h, 0, j}] - E^((I c^2)/(4 d) - g) Sum[(-1)^(-h + j) 4^j (-c)^(-h - j + 2 n) (-c + 2 I d Sqrt[z])^(h + j) ((I (-c + 2 I d Sqrt[z])^2)/d)^ ((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] ((-c) (-c + 2 I d Sqrt[z]) Gamma[(1/2) (1 + h + j), (I (-c + 2 I d Sqrt[z])^2)/(4 d)] + 2 I d Sqrt[(I (-c + 2 I d Sqrt[z])^2)/d] Gamma[(1/2) (2 + h + j), (I (-c + 2 I d Sqrt[z])^2)/(4 d)]), {j, 0, n}, {h, 0, j}] - E^((I c^2)/(4 d) + g) Sum[(-1)^(-h + j) 4^j c^(-h - j + 2 n) (c + 2 I d Sqrt[z])^(h + j) ((I (c + 2 I d Sqrt[z])^2)/d)^ ((1/2) (-1 - h - j)) Binomial[j, h] Binomial[n, j] (c (c + 2 I d Sqrt[z]) Gamma[(1/2) (1 + h + j), (I (c + 2 I d Sqrt[z])^2)/(4 d)] + 2 I d Sqrt[(I (c + 2 I d Sqrt[z])^2)/d] Gamma[(1/2) (2 + h + j), (I (c + 2 I d Sqrt[z])^2)/(4 d)]), {j, 0, n}, {h, 0, j}]))/ d^(2 (1 + n)) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n sin ( d z ) cosh ( z c + g ) z ( - 1 ) n - 1 2 - 2 n - 3 d - 2 ( n + 1 ) ( - c 2 4 d - g j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - c ) - h - j + 2 n ( 2 d z - c ) h + j ( ( 2 d z - c ) 2 d ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 d ( 2 d z - c ) 2 d Γ ( 1 2 ( h + j + 2 ) , ( 2 d z - c ) 2 4 d ) - c ( 2 d z - c ) Γ ( 1 2 ( h + j + 1 ) , ( 2 d z - c ) 2 4 d ) ) - c 2 4 d + g j = 0 n h = 0 j ( - 1 ) j - h 4 j c - h - j + 2 n ( c + 2 d z ) h + j ( ( c + 2 d z ) 2 d ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( c + 2 d z ) Γ ( 1 2 ( h + j + 1 ) , ( c + 2 d z ) 2 4 d ) + 2 ( c + 2 d z ) 2 d d Γ ( 1 2 ( h + j + 2 ) , ( c + 2 d z ) 2 4 d ) ) + - c 2 4 d - g j = 0 n h = 0 j ( - 1 ) j - h 4 j ( - c ) - h - j + 2 n ( - c - 2 d z ) h + j ( - ( - c - 2 d z ) 2 d ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - c ( - c - 2 d z ) Γ ( 1 2 ( h + j + 1 ) , - ( - c - 2 d z ) 2 4 d ) - 2 d - ( - c - 2 d z ) 2 d Γ ( 1 2 ( h + j + 2 ) , - ( - c - 2 d z ) 2 4 d ) ) + - c 2 4 d + g j = 0 n h = 0 j ( - 1 ) j - h 4 j c - h - j + 2 n ( c - 2 d z ) h + j ( - ( c - 2 d z ) 2 d ) 1 2 ( - h - j - 1 ) ( j h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["j", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c ( c - 2 d z ) Γ ( 1 2 ( h + j + 1 ) , - ( c - 2 d z ) 2 4 d ) - 2 d - ( c - 2 d z ) 2 d Γ ( 1 2 ( h + j + 2 ) , - ( c - 2 d z ) 2 4 d ) ) ) /; n Condition z z n d z z 1 2 c g -1 n -1 2 -2 n -3 d -2 n 1 -1 c 2 4 d -1 -1 g h 0 j j 0 n -1 j -1 h 4 j -1 c -1 h -1 j 2 n 2 d z 1 2 -1 c h j 2 d z 1 2 -1 c 2 d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j 2 d 2 d z 1 2 -1 c 2 d -1 1 2 Gamma 1 2 h j 2 2 d z 1 2 -1 c 2 4 d -1 -1 c 2 d z 1 2 -1 c Gamma 1 2 h j 1 2 d z 1 2 -1 c 2 4 d -1 -1 c 2 4 d -1 g h 0 j j 0 n -1 j -1 h 4 j c -1 h -1 j 2 n c 2 d z 1 2 h j c 2 d z 1 2 2 d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c c 2 d z 1 2 Gamma 1 2 h j 1 c 2 d z 1 2 2 4 d -1 2 c 2 d z 1 2 2 d -1 1 2 d Gamma 1 2 h j 2 c 2 d z 1 2 2 4 d -1 -1 c 2 4 d -1 -1 g h 0 j j 0 n -1 j -1 h 4 j -1 c -1 h -1 j 2 n -1 c -1 2 d z 1 2 h j -1 -1 c -1 2 d z 1 2 2 d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j -1 c -1 c -1 2 d z 1 2 Gamma 1 2 h j 1 -1 -1 c -1 2 d z 1 2 2 4 d -1 -1 2 d -1 -1 c -1 2 d z 1 2 2 d -1 1 2 Gamma 1 2 h j 2 -1 -1 c -1 2 d z 1 2 2 4 d -1 -1 c 2 4 d -1 g h 0 j j 0 n -1 j -1 h 4 j c -1 h -1 j 2 n c -1 2 d z 1 2 h j -1 c -1 2 d z 1 2 2 d -1 1 2 -1 h -1 j -1 Binomial j h Binomial n j c c -1 2 d z 1 2 Gamma 1 2 h j 1 -1 c -1 2 d z 1 2 2 4 d -1 -1 2 d -1 c -1 2 d z 1 2 2 d -1 1 2 Gamma 1 2 h j 2 -1 c -1 2 d z 1 2 2 4 d -1 n [/itex]

 Rule Form

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

 2002-12-18