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/01.20.21.1452.01

 Input Form

 Integrate[z^n E^(b Sqrt[z] + d z + e) Cos[a Sqrt[z] + p z + q]^m Cosh[c Sqrt[z] + f z + g], z] == 2^(-2 - m - 2 n) Binomial[m, m/2] (1 - Mod[m, 2]) (E^(e - (b - c)^2/(4 (d - f)) - g) (d - f)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (b - c)^(-h - i + 2 n) (b - c + 2 (d - f) Sqrt[z])^(h + i) (-((b - c + 2 (d - f) Sqrt[z])^2/(d - f)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((b - c) (b - c + 2 (d - f) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((b - c + 2 (d - f) Sqrt[z])^2/ (4 (d - f)))] + 2 (d - f) Sqrt[-((b - c + 2 (d - f) Sqrt[z])^2/ (d - f))] Gamma[(1/2) (2 + h + i), -((b - c + 2 (d - f) Sqrt[z])^2/(4 (d - f)))]), {i, 0, n}, {h, 0, i}] + E^(e - (b + c)^2/(4 (d + f)) + g) (d + f)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (b + c)^(-h - i + 2 n) (b + c + 2 (d + f) Sqrt[z])^(h + i) (-((b + c + 2 (d + f) Sqrt[z])^2/(d + f)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((b + c) (b + c + 2 (d + f) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((b + c + 2 (d + f) Sqrt[z])^2/ (4 (d + f)))] + 2 (d + f) Sqrt[-((b + c + 2 (d + f) Sqrt[z])^2/ (d + f))] Gamma[(1/2) (2 + h + i), -((b + c + 2 (d + f) Sqrt[z])^2/(4 (d + f)))]), {i, 0, n}, {h, 0, i}]) + 2^(-2 - m - 2 n) Sum[Binomial[m, k] (E^(e - g - (b - c + I a (2 k - m))^2/ (4 (d - f + I (2 k - m) p)) + I (2 k - m) q) (d - f + I (2 k - m) p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (b - c + I a (2 k - m))^(-h - i + 2 n) (b - c + I a (2 k - m) + 2 (d - f + I (2 k - m) p) Sqrt[z])^(h + i) (-((b - c + I a (2 k - m) + 2 (d - f + I (2 k - m) p) Sqrt[z])^2/ (d - f + I (2 k - m) p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((b - c + I a (2 k - m)) (b - c + I a (2 k - m) + 2 (d - f + I (2 k - m) p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((b - c + I a (2 k - m) + 2 (d - f + I (2 k - m) p) Sqrt[z])^2/( 4 (d - f + I (2 k - m) p)))] + 2 (d - f + I (2 k - m) p) Sqrt[-((b - c + I a (2 k - m) + 2 (d - f + I (2 k - m) p) Sqrt[z])^2/(d - f + I (2 k - m) p))] Gamma[(1/2) (2 + h + i), -((b - c + I a (2 k - m) + 2 (d - f + I (2 k - m) p) Sqrt[z])^2/(4 (d - f + I (2 k - m) p)))]), {i, 0, n}, {h, 0, i}] + E^(e + g - (b + c + I a (2 k - m))^2/(4 (d + f + I (2 k - m) p)) + I (2 k - m) q) (d + f + I (2 k - m) p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (b + c + I a (2 k - m))^(-h - i + 2 n) (b + c + I a (2 k - m) + 2 (d + f + I (2 k - m) p) Sqrt[z])^(h + i) (-((b + c + I a (2 k - m) + 2 (d + f + I (2 k - m) p) Sqrt[z])^2/ (d + f + I (2 k - m) p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((b + c + I a (2 k - m)) (b + c + I a (2 k - m) + 2 (d + f + I (2 k - m) p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((b + c + I a (2 k - m) + 2 (d + f + I (2 k - m) p) Sqrt[z])^2/( 4 (d + f + I (2 k - m) p)))] + 2 (d + f + I (2 k - m) p) Sqrt[-((b + c + I a (2 k - m) + 2 (d + f + I (2 k - m) p) Sqrt[z])^2/(d + f + I (2 k - m) p))] Gamma[(1/2) (2 + h + i), -((b + c + I a (2 k - m) + 2 (d + f + I (2 k - m) p) Sqrt[z])^2/(4 (d + f + I (2 k - m) p)))]), {i, 0, n}, {h, 0, i}] + E^(e - g - (b - c + I a (-2 k + m))^2/(4 (d - f + I (-2 k + m) p)) + I (-2 k + m) q) (d - f + I (-2 k + m) p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (b - c + I a (-2 k + m))^(-h - i + 2 n) (b - c + I a (-2 k + m) + 2 (d - f + I (-2 k + m) p) Sqrt[z])^ (h + i) (-((b - c + I a (-2 k + m) + 2 (d - f + I (-2 k + m) p) Sqrt[z])^2/(d - f + I (-2 k + m) p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((b - c + I a (-2 k + m)) (b - c + I a (-2 k + m) + 2 (d - f + I (-2 k + m) p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((b - c + I a (-2 k + m) + 2 (d - f + I (-2 k + m) p) Sqrt[z])^2/(4 (d - f + I (-2 k + m) p)))] + 2 (d - f + I (-2 k + m) p) Sqrt[-((b - c + I a (-2 k + m) + 2 (d - f + I (-2 k + m) p) Sqrt[z])^2/(d - f + I (-2 k + m) p))] Gamma[(1/2) (2 + h + i), -((b - c + I a (-2 k + m) + 2 (d - f + I (-2 k + m) p) Sqrt[z])^2/(4 (d - f + I (-2 k + m) p)))]), {i, 0, n}, {h, 0, i}] + E^(e + g - (b + c + I a (-2 k + m))^2/(4 (d + f + I (-2 k + m) p)) + I (-2 k + m) q) (d + f + I (-2 k + m) p)^(-2 - 2 n) Sum[(-1)^(-h + i) 4^i (b + c + I a (-2 k + m))^(-h - i + 2 n) (b + c + I a (-2 k + m) + 2 (d + f + I (-2 k + m) p) Sqrt[z])^ (h + i) (-((b + c + I a (-2 k + m) + 2 (d + f + I (-2 k + m) p) Sqrt[z])^2/(d + f + I (-2 k + m) p)))^((1/2) (-1 - h - i)) Binomial[i, h] Binomial[n, i] ((b + c + I a (-2 k + m)) (b + c + I a (-2 k + m) + 2 (d + f + I (-2 k + m) p) Sqrt[z]) Gamma[(1/2) (1 + h + i), -((b + c + I a (-2 k + m) + 2 (d + f + I (-2 k + m) p) Sqrt[z])^2/(4 (d + f + I (-2 k + m) p)))] + 2 (d + f + I (-2 k + m) p) Sqrt[-((b + c + I a (-2 k + m) + 2 (d + f + I (-2 k + m) p) Sqrt[z])^2/(d + f + I (-2 k + m) p))] Gamma[(1/2) (2 + h + i), -((b + c + I a (-2 k + m) + 2 (d + f + I (-2 k + m) p) Sqrt[z])^2/(4 (d + f + I (-2 k + m) p)))]), {i, 0, n}, {h, 0, i}]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 z n z b + d z + e cos m ( z a + p z + q ) cosh ( z c + f z + g ) z 2 - m - 2 n - 2 ( 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( - ( b - c ) 2 4 ( d - f ) + e - g ( d - f ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - c ) - h - i + 2 n ( b - c + 2 ( d - f ) z ) h + i ( - ( b - c + 2 ( d - f ) z ) 2 d - f ) 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 ) ( b - c + 2 ( d - f ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b - c + 2 ( d - f ) z ) 2 4 ( d - f ) ) + 2 - ( b - c + 2 ( d - f ) z ) 2 d - f ( d - f ) Γ ( 1 2 ( h + i + 2 ) , - ( b - c + 2 ( d - f ) z ) 2 4 ( d - f ) ) ) + - ( b + c ) 2 4 ( d + f ) + e + g ( d + f ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b + c ) - h - i + 2 n ( b + c + 2 ( d + f ) z ) h + i ( - ( b + c + 2 ( d + f ) z ) 2 d + f ) 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 ) ( b + c + 2 ( d + f ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b + c + 2 ( d + f ) z ) 2 4 ( d + f ) ) + 2 - ( b + c + 2 ( d + f ) z ) 2 d + f ( d + f ) Γ ( 1 2 ( h + i + 2 ) , - ( b + c + 2 ( d + f ) z ) 2 4 ( d + f ) ) ) ) + 2 - m - 2 n - 2 k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( b - c + a ( 2 k - m ) ) 2 4 ( d - f + ( 2 k - m ) p ) + e - g + ( 2 k - m ) q ( d - f + ( 2 k - m ) p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - c + a ( 2 k - m ) ) - h - i + 2 n ( b - c + a ( 2 k - m ) + 2 ( d - f + ( 2 k - m ) p ) z ) h + i ( - ( b - c + a ( 2 k - m ) + 2 ( d - f + ( 2 k - m ) p ) z ) 2 d - f + ( 2 k - m ) 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 + a ( 2 k - m ) ) ( b - c + a ( 2 k - m ) + 2 ( d - f + ( 2 k - m ) p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b - c + a ( 2 k - m ) + 2 ( d - f + ( 2 k - m ) p ) z ) 2 4 ( d - f + ( 2 k - m ) p ) ) + 2 ( d - f + ( 2 k - m ) p ) Γ ( 1 2 ( h + i + 2 ) , - ( b - c + a ( 2 k - m ) + 2 ( d - f + ( 2 k - m ) p ) z ) 2 4 ( d - f + ( 2 k - m ) p ) ) - ( b - c + a ( 2 k - m ) + 2 ( d - f + ( 2 k - m ) p ) z ) 2 d - f + ( 2 k - m ) p ) + - ( b + c + a ( 2 k - m ) ) 2 4 ( d + f + ( 2 k - m ) p ) + e + g + ( 2 k - m ) q ( d + f + ( 2 k - m ) p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b + c + a ( 2 k - m ) ) - h - i + 2 n ( b + c + a ( 2 k - m ) + 2 ( d + f + ( 2 k - m ) p ) z ) h + i ( - ( b + c + a ( 2 k - m ) + 2 ( d + f + ( 2 k - m ) p ) z ) 2 d + f + ( 2 k - m ) 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 + a ( 2 k - m ) ) ( b + c + a ( 2 k - m ) + 2 ( d + f + ( 2 k - m ) p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b + c + a ( 2 k - m ) + 2 ( d + f + ( 2 k - m ) p ) z ) 2 4 ( d + f + ( 2 k - m ) p ) ) + 2 ( d + f + ( 2 k - m ) p ) Γ ( 1 2 ( h + i + 2 ) , - ( b + c + a ( 2 k - m ) + 2 ( d + f + ( 2 k - m ) p ) z ) 2 4 ( d + f + ( 2 k - m ) p ) ) - ( b + c + a ( 2 k - m ) + 2 ( d + f + ( 2 k - m ) p ) z ) 2 d + f + ( 2 k - m ) p ) + - ( b - c + a ( m - 2 k ) ) 2 4 ( d - f + ( m - 2 k ) p ) + e - g + ( m - 2 k ) q ( d - f + ( m - 2 k ) p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b - c + a ( m - 2 k ) ) - h - i + 2 n ( b - c + a ( m - 2 k ) + 2 ( d - f + ( m - 2 k ) p ) z ) h + i ( - ( b - c + a ( m - 2 k ) + 2 ( d - f + ( m - 2 k ) p ) z ) 2 d - f + ( m - 2 k ) 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 + a ( m - 2 k ) ) ( b - c + a ( m - 2 k ) + 2 ( d - f + ( m - 2 k ) p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b - c + a ( m - 2 k ) + 2 ( d - f + ( m - 2 k ) p ) z ) 2 4 ( d - f + ( m - 2 k ) p ) ) + 2 ( d - f + ( m - 2 k ) p ) Γ ( 1 2 ( h + i + 2 ) , - ( b - c + a ( m - 2 k ) + 2 ( d - f + ( m - 2 k ) p ) z ) 2 4 ( d - f + ( m - 2 k ) p ) ) - ( b - c + a ( m - 2 k ) + 2 ( d - f + ( m - 2 k ) p ) z ) 2 d - f + ( m - 2 k ) p ) + - ( b + c + a ( m - 2 k ) ) 2 4 ( d + f + ( m - 2 k ) p ) + e + g + ( m - 2 k ) q ( d + f + ( m - 2 k ) p ) - 2 n - 2 i = 0 n h = 0 i ( - 1 ) i - h 4 i ( b + c + a ( m - 2 k ) ) - h - i + 2 n ( b + c + a ( m - 2 k ) + 2 ( d + f + ( m - 2 k ) p ) z ) h + i ( - ( b + c + a ( m - 2 k ) + 2 ( d + f + ( m - 2 k ) p ) z ) 2 d + f + ( m - 2 k ) 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 + a ( m - 2 k ) ) ( b + c + a ( m - 2 k ) + 2 ( d + f + ( m - 2 k ) p ) z ) Γ ( 1 2 ( h + i + 1 ) , - ( b + c + a ( m - 2 k ) + 2 ( d + f + ( m - 2 k ) p ) z ) 2 4 ( d + f + ( m - 2 k ) p ) ) + 2 ( d + f + ( m - 2 k ) p ) Γ ( 1 2 ( h + i + 2 ) , - ( b + c + a ( m - 2 k ) + 2 ( d + f + ( m - 2 k ) p ) z ) 2 4 ( d + f + ( m - 2 k ) p ) ) - ( b + c + a ( m - 2 k ) + 2 ( d + f + ( m - 2 k ) p ) z ) 2 d + f + ( m - 2 k ) p ) ) /; n m + Condition z z n z 1 2 b d z e z 1 2 a p z q m z 1 2 c f z g 2 -1 m -1 2 n -2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 -1 b -1 c 2 4 d -1 f -1 e -1 g d -1 f -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b -1 c -1 h -1 i 2 n b -1 c 2 d -1 f z 1 2 h i -1 b -1 c 2 d -1 f z 1 2 2 d -1 f -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 c b -1 c 2 d -1 f z 1 2 Gamma 1 2 h i 1 -1 b -1 c 2 d -1 f z 1 2 2 4 d -1 f -1 2 -1 b -1 c 2 d -1 f z 1 2 2 d -1 f -1 1 2 d -1 f Gamma 1 2 h i 2 -1 b -1 c 2 d -1 f z 1 2 2 4 d -1 f -1 -1 b c 2 4 d f -1 e g d f -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b c -1 h -1 i 2 n b c 2 d f z 1 2 h i -1 b c 2 d f z 1 2 2 d f -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b c b c 2 d f z 1 2 Gamma 1 2 h i 1 -1 b c 2 d f z 1 2 2 4 d f -1 2 -1 b c 2 d f z 1 2 2 d f -1 1 2 d f Gamma 1 2 h i 2 -1 b c 2 d f z 1 2 2 4 d f -1 2 -1 m -1 2 n -2 k 0 m -1 2 -1 Binomial m k -1 b -1 c a 2 k -1 m 2 4 d -1 f 2 k -1 m p -1 e -1 g 2 k -1 m q d -1 f 2 k -1 m p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b -1 c a 2 k -1 m -1 h -1 i 2 n b -1 c a 2 k -1 m 2 d -1 f 2 k -1 m p z 1 2 h i -1 b -1 c a 2 k -1 m 2 d -1 f 2 k -1 m p z 1 2 2 d -1 f 2 k -1 m p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 c a 2 k -1 m b -1 c a 2 k -1 m 2 d -1 f 2 k -1 m p z 1 2 Gamma 1 2 h i 1 -1 b -1 c a 2 k -1 m 2 d -1 f 2 k -1 m p z 1 2 2 4 d -1 f 2 k -1 m p -1 2 d -1 f 2 k -1 m p Gamma 1 2 h i 2 -1 b -1 c a 2 k -1 m 2 d -1 f 2 k -1 m p z 1 2 2 4 d -1 f 2 k -1 m p -1 -1 b -1 c a 2 k -1 m 2 d -1 f 2 k -1 m p z 1 2 2 d -1 f 2 k -1 m p -1 1 2 -1 b c a 2 k -1 m 2 4 d f 2 k -1 m p -1 e g 2 k -1 m q d f 2 k -1 m p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b c a 2 k -1 m -1 h -1 i 2 n b c a 2 k -1 m 2 d f 2 k -1 m p z 1 2 h i -1 b c a 2 k -1 m 2 d f 2 k -1 m p z 1 2 2 d f 2 k -1 m p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b c a 2 k -1 m b c a 2 k -1 m 2 d f 2 k -1 m p z 1 2 Gamma 1 2 h i 1 -1 b c a 2 k -1 m 2 d f 2 k -1 m p z 1 2 2 4 d f 2 k -1 m p -1 2 d f 2 k -1 m p Gamma 1 2 h i 2 -1 b c a 2 k -1 m 2 d f 2 k -1 m p z 1 2 2 4 d f 2 k -1 m p -1 -1 b c a 2 k -1 m 2 d f 2 k -1 m p z 1 2 2 d f 2 k -1 m p -1 1 2 -1 b -1 c a m -1 2 k 2 4 d -1 f m -1 2 k p -1 e -1 g m -1 2 k q d -1 f m -1 2 k p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b -1 c a m -1 2 k -1 h -1 i 2 n b -1 c a m -1 2 k 2 d -1 f m -1 2 k p z 1 2 h i -1 b -1 c a m -1 2 k 2 d -1 f m -1 2 k p z 1 2 2 d -1 f m -1 2 k p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b -1 c a m -1 2 k b -1 c a m -1 2 k 2 d -1 f m -1 2 k p z 1 2 Gamma 1 2 h i 1 -1 b -1 c a m -1 2 k 2 d -1 f m -1 2 k p z 1 2 2 4 d -1 f m -1 2 k p -1 2 d -1 f m -1 2 k p Gamma 1 2 h i 2 -1 b -1 c a m -1 2 k 2 d -1 f m -1 2 k p z 1 2 2 4 d -1 f m -1 2 k p -1 -1 b -1 c a m -1 2 k 2 d -1 f m -1 2 k p z 1 2 2 d -1 f m -1 2 k p -1 1 2 -1 b c a m -1 2 k 2 4 d f m -1 2 k p -1 e g m -1 2 k q d f m -1 2 k p -2 n -2 h 0 i i 0 n -1 i -1 h 4 i b c a m -1 2 k -1 h -1 i 2 n b c a m -1 2 k 2 d f m -1 2 k p z 1 2 h i -1 b c a m -1 2 k 2 d f m -1 2 k p z 1 2 2 d f m -1 2 k p -1 1 2 -1 h -1 i -1 Binomial i h Binomial n i b c a m -1 2 k b c a m -1 2 k 2 d f m -1 2 k p z 1 2 Gamma 1 2 h i 1 -1 b c a m -1 2 k 2 d f m -1 2 k p z 1 2 2 4 d f m -1 2 k p -1 2 d f m -1 2 k p Gamma 1 2 h i 2 -1 b c a m -1 2 k 2 d f m -1 2 k p z 1 2 2 4 d f m -1 2 k p -1 -1 b c a m -1 2 k 2 d f m -1 2 k p z 1 2 2 d f m -1 2 k p -1 1 2 n m SuperPlus [/itex]

 Rule Form

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

 2002-12-18