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/01.20.21.1417.01

 Input Form

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

 Standard Form

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 MathML Form

 z n p z cos ( b z ) cosh ( c z ) z 2 - 2 n - 3 p - 2 ( n + 1 ) ( - ( - c - b ) 2 4 p i = 0 n h = 0 i ( - 1 ) i - h 4 i ( - c - b ) - h - i + 2 n ( - c - b + 2 p z ) h + i ( - ( - c - b + 2 p z ) 2 p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - c - b ) ( - c - b + 2 p z ) Γ ( 1 2 ( h + i + 1 ) , - ( - c - b + 2 p z ) 2 4 p ) + 2 - ( - c - b + 2 p z ) 2 p p Γ ( 1 2 ( h + i + 2 ) , - ( - c - b + 2 p z ) 2 4 p ) ) + - ( b - c ) 2 4 p i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - c ) - h - i + 2 n ( - c + b + 2 p z ) h + i ( - ( - c + b + 2 p z ) 2 p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( b - c ) ( - c + b + 2 p z ) Γ ( 1 2 ( h + i + 1 ) , - ( - c + b + 2 p z ) 2 4 p ) + 2 - ( - c + b + 2 p z ) 2 p p Γ ( 1 2 ( h + i + 2 ) , - ( - c + b + 2 p z ) 2 4 p ) ) + - ( c - b ) 2 4 p i = 0 n h = 0 i ( - 1 ) i - h 4 i ( c - b ) - h - i + 2 n ( c - b + 2 p z ) h + i ( - ( c - b + 2 p z ) 2 p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( c - b ) ( c - b + 2 p z ) Γ ( 1 2 ( h + i + 1 ) , - ( c - b + 2 p z ) 2 4 p ) + 2 - ( c - b + 2 p z ) 2 p p Γ ( 1 2 ( h + i + 2 ) , - ( c - b + 2 p z ) 2 4 p ) ) + - ( c + b ) 2 4 p i = 0 n h = 0 i ( - 1 ) i - h 4 i ( c + b ) - h - i + 2 n ( c + b + 2 p z ) h + i ( - ( c + b + 2 p z ) 2 p ) 1 2 ( - h - i - 1 ) ( i h ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["i", Identity]], List[TagBox["h", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( n i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( c + b ) ( c + b + 2 p z ) Γ ( 1 2 ( h + i + 1 ) , - ( c + b + 2 p z ) 2 4 p ) + 2 - ( c + b + 2 p z ) 2 p p Γ ( 1 2 ( h + i + 2 ) , - ( c + b + 2 p z ) 2 4 p ) ) ) /; v + n Condition z z n p z b z 1 2 c z 1 2 2 -2 n -3 p -2 n 1 -1 -1 c -1 b 2 4 p -1 h 0 i i 0 n -1 i -1 h 4 i -1 c -1 b -1 h -1 i 2 n -1 c -1 b 2 p z 1 2 h i -1 -1 c -1 b 2 p z 1 2 2 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i -1 c -1 b -1 c -1 b 2 p z 1 2 Gamma 1 2 h i 1 -1 -1 c -1 b 2 p z 1 2 2 4 p -1 2 -1 -1 c -1 b 2 p z 1 2 2 p -1 1 2 p Gamma 1 2 h i 2 -1 -1 c -1 b 2 p z 1 2 2 4 p -1 -1 b -1 c 2 4 p -1 h 0 i i 0 n -1 i -1 h 4 i b -1 c -1 h -1 i 2 n -1 c b 2 p z 1 2 h i -1 -1 c b 2 p z 1 2 2 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 c -1 c b 2 p z 1 2 Gamma 1 2 h i 1 -1 -1 c b 2 p z 1 2 2 4 p -1 2 -1 -1 c b 2 p z 1 2 2 p -1 1 2 p Gamma 1 2 h i 2 -1 -1 c b 2 p z 1 2 2 4 p -1 -1 c -1 b 2 4 p -1 h 0 i i 0 n -1 i -1 h 4 i c -1 b -1 h -1 i 2 n c -1 b 2 p z 1 2 h i -1 c -1 b 2 p z 1 2 2 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i c -1 b c -1 b 2 p z 1 2 Gamma 1 2 h i 1 -1 c -1 b 2 p z 1 2 2 4 p -1 2 -1 c -1 b 2 p z 1 2 2 p -1 1 2 p Gamma 1 2 h i 2 -1 c -1 b 2 p z 1 2 2 4 p -1 -1 c b 2 4 p -1 h 0 i i 0 n -1 i -1 h 4 i c b -1 h -1 i 2 n c b 2 p z 1 2 h i -1 c b 2 p z 1 2 2 p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i c b c b 2 p z 1 2 Gamma 1 2 h i 1 -1 c b 2 p z 1 2 2 4 p -1 2 -1 c b 2 p z 1 2 2 p -1 1 2 p Gamma 1 2 h i 2 -1 c b 2 p z 1 2 2 4 p -1 v SuperPlus n [/itex]

 Rule Form

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

 2002-12-18