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/01.20.21.4072.01

 Input Form

 Integrate[Sinh[b Sqrt[z] + d z] Cosh[c Sqrt[z]]^v, z] == 2^(-2 - v) Binomial[v, v/2] ((4 Cosh[b Sqrt[z] + d z])/d + (b E^(b^2/(4 d)) Sqrt[Pi] Erfi[(b + 2 d Sqrt[z])/(2 Sqrt[-d])])/ (-d)^(3/2) - (b Sqrt[Pi] Erfi[(b + 2 d Sqrt[z])/(2 Sqrt[d])])/ (E^(b^2/(4 d)) d^(3/2))) (1 - Mod[v, 2]) + 2^(-2 - v) Sum[Binomial[v, s] ((8 Cosh[c (2 s - v) Sqrt[z]] Cosh[b Sqrt[z] + d z])/d + (1/(-d)^(3/2)) (E^((-b + c (-2 s + v))^2/(4 d)) Sqrt[Pi] (-b + c (-2 s + v)) Erfi[(-b + c (-2 s + v) - 2 d Sqrt[z])/(2 Sqrt[-d])]) - (1/d^(3/2)) ((Sqrt[Pi] (-b + c (-2 s + v)) Erfi[(-b + c (-2 s + v) - 2 d Sqrt[z])/(2 Sqrt[d])])/ E^((b - c (-2 s + v))^2/(4 d))) + (1/(-d)^(3/2)) (E^((-b - c (-2 s + v))^2/(4 d)) Sqrt[Pi] (b + c (-2 s + v)) Erfi[(b + c (-2 s + v) + 2 d Sqrt[z])/(2 Sqrt[-d])]) - (1/d^(3/2)) ((Sqrt[Pi] (b + c (-2 s + v)) Erfi[(b + c (-2 s + v) + 2 d Sqrt[z])/(2 Sqrt[d])])/ E^((b + c (-2 s + v))^2/(4 d)))), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 sinh ( z b + d z ) cosh v ( c z ) z 2 - v - 2 ( 4 cosh ( z b + d z ) d + b b 2 4 d π erfi ( b + 2 d z 2 - d ) ( - d ) 3 / 2 - b - b 2 4 d π erfi ( b + 2 d z 2 d ) d 3 / 2 ) ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - v - 2 s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 8 cosh ( c ( 2 s - v ) z ) cosh ( z b + d z ) d + ( - b - c ( v - 2 s ) ) 2 4 d π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 d z 2 - d ) ( - d ) 3 / 2 + ( c ( v - 2 s ) - b ) 2 4 d π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) - 2 d z 2 - d ) ( - d ) 3 / 2 - - ( b + c ( v - 2 s ) ) 2 4 d π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 d z 2 d ) d 3 / 2 - - ( b - c ( v - 2 s ) ) 2 4 d π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) - 2 d z 2 d ) d 3 / 2 ) /; v + Condition z z 1 2 b d z c z 1 2 v 2 -1 v -2 4 z 1 2 b d z d -1 b b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 b -1 b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s 8 c 2 s -1 v z 1 2 z 1 2 b d z d -1 -1 b -1 c v -1 2 s 2 4 d -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 c v -1 2 s -1 b 2 4 d -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s -1 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 -1 b c v -1 2 s 2 4 d -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 -1 -1 b -1 c v -1 2 s 2 4 d -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s -1 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18