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/01.20.21.3687.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18