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/01.20.21.4113.01

 Input Form

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

 Standard Form

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 MathML Form

 sinh ( z b + e + d z ) cosh v ( z c + g + f z ) z 2 - v - 2 ( 2 - d z - b z ( 1 + 2 ( z b + e + d z ) ) d + b b 2 4 d π erfi ( b + 2 d z 2 - d ) ( - d ) 3 / 2 - b 2 e - b 2 4 d π erfi ( b + 2 d z 2 d ) d 3 / 2 ) - e ( 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]]]]] ( e - g ( v - 2 s ) ( ( 2 ( g ( v - 2 s ) - e ) - ( c ( v - 2 s ) - b ) 2 4 ( f ( v - 2 s ) - d ) π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z 2 f ( v - 2 s ) - d ) ) / ( f ( v - 2 s ) - d ) 3 / 2 - 2 z ( c ( v - 2 s ) - b ) + 2 ( g ( v - 2 s ) - e ) + ( f ( v - 2 s ) - d ) z f ( v - 2 s ) - d + 2 z ( b - c ( v - 2 s ) ) + ( d - f ( v - 2 s ) ) z d - f ( v - 2 s ) - - ( b - c ( v - 2 s ) ) 2 4 ( d - f ( v - 2 s ) ) π ( c ( v - 2 s ) - b ) erfi ( - b + c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z 2 d - f ( v - 2 s ) ) ( d - f ( v - 2 s ) ) 3 / 2 ) - - e - g ( v - 2 s ) ( ( 2 ( e + g ( v - 2 s ) ) - ( b + c ( v - 2 s ) ) 2 4 ( d + f ( v - 2 s ) ) π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z 2 d + f ( v - 2 s ) ) ) / ( d + f ( v - 2 s ) ) 3 / 2 - 2 z ( b + c ( v - 2 s ) ) + 2 ( e + g ( v - 2 s ) ) + ( d + f ( v - 2 s ) ) z d + f ( v - 2 s ) + 2 z ( - b - c ( v - 2 s ) ) + ( - d - f ( v - 2 s ) ) z - d - f ( v - 2 s ) - - ( - b - c ( v - 2 s ) ) 2 4 ( - d - f ( v - 2 s ) ) π ( b + c ( v - 2 s ) ) erfi ( b + c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z 2 - d - f ( v - 2 s ) ) ( - d - f ( v - 2 s ) ) 3 / 2 ) ) /; v + Condition z z 1 2 b e d z z 1 2 c g f z v 2 -1 v -2 2 -1 d z -1 b z 1 2 1 2 z 1 2 b e 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 2 e -1 b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 -1 e Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s e -1 g v -1 2 s 2 g v -1 2 s -1 e -1 c v -1 2 s -1 b 2 4 f v -1 2 s -1 d -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 f v -1 2 s -1 d 1 2 -1 f v -1 2 s -1 d 3 2 -1 -1 2 z 1 2 c v -1 2 s -1 b 2 g v -1 2 s -1 e f v -1 2 s -1 d z f v -1 2 s -1 d -1 2 z 1 2 b -1 c v -1 2 s d -1 f v -1 2 s z d -1 f v -1 2 s -1 -1 -1 b -1 c v -1 2 s 2 4 d -1 f v -1 2 s -1 1 2 c v -1 2 s -1 b Erfi -1 b c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 d -1 f v -1 2 s 1 2 -1 d -1 f v -1 2 s 3 2 -1 -1 -1 e -1 g v -1 2 s 2 e g v -1 2 s -1 b c v -1 2 s 2 4 d f v -1 2 s -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 d f v -1 2 s z 1 2 2 d f v -1 2 s 1 2 -1 d f v -1 2 s 3 2 -1 -1 2 z 1 2 b c v -1 2 s 2 e g v -1 2 s d f v -1 2 s z d f v -1 2 s -1 2 z 1 2 -1 b -1 c v -1 2 s -1 d -1 f v -1 2 s z -1 d -1 f v -1 2 s -1 -1 -1 -1 b -1 c v -1 2 s 2 4 -1 d -1 f v -1 2 s -1 1 2 b c v -1 2 s Erfi b c v -1 2 s 2 d f v -1 2 s z 1 2 2 -1 d -1 f v -1 2 s 1 2 -1 -1 d -1 f v -1 2 s 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18