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; }

 InverseGammaRegularized

 http://functions.wolfram.com/06.12.20.0011.01

 Input Form

 D[InverseGammaRegularized[a, z], {z, 9}] == (-E^(9 w)) w^(1 - 9 a) (1 + a (-36 + a (546 + a (-4536 + a (22449 + 4 a (-16821 + a (29531 + 36 a (-761 + 280 a))))))) + 502 w - 2 a (4679 + a (-36893 + a (159365 + 4 a (-101576 + a (152039 + 36 a (-3403 + 1120 a)))))) w + 2 (-1 + a) (-1 + 2 a) (9511 + a (-87099 + 4 a (75437 + 45 a (-2619 + 1568 a)))) w^2 - 8 (-1 + a) (-1 + 2 a) (-23411 + 4 a (31337 + 45 a (-1265 + 784 a))) w^3 + 4 (-1 + a) (-175291 + a (829183 + 180 a (-7323 + 3920 a))) w^4 - 8 (-1 + a) (146221 + 36 a (-11243 + 7840 a)) w^5 + 144 (-1 + a) (-6361 + 7840 a) w^6 - 322560 (-1 + a) w^7 + 40320 w^8) Gamma[a]^9 /; w == InverseGammaRegularized[a, z]

 Standard Form

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 MathML Form

 9 Q GammaRegularized - 1 ( a , z ) z 9 - 9 w w 1 - 9 a ( 40320 w 8 - 322560 ( a - 1 ) w 7 + 144 ( a - 1 ) ( 7840 a - 6361 ) w 6 - 8 ( a - 1 ) ( 36 a ( 7840 a - 11243 ) + 146221 ) w 5 + 4 ( a - 1 ) ( a ( 180 a ( 3920 a - 7323 ) + 829183 ) - 175291 ) w 4 - 8 ( a - 1 ) ( 2 a - 1 ) ( 4 a ( 45 a ( 784 a - 1265 ) + 31337 ) - 23411 ) w 3 + 2 ( a - 1 ) ( 2 a - 1 ) ( a ( 4 a ( 45 a ( 1568 a - 2619 ) + 75437 ) - 87099 ) + 9511 ) w 2 - 2 a ( a ( a ( 4 a ( a ( 36 a ( 1120 a - 3403 ) + 152039 ) - 101576 ) + 159365 ) - 36893 ) + 4679 ) w + 502 w + a ( a ( a ( a ( 4 a ( a ( 36 a ( 280 a - 761 ) + 29531 ) - 16821 ) + 22449 ) - 4536 ) + 546 ) - 36 ) + 1 ) Γ ( a ) 9 /; w Q GammaRegularized - 1 ( a , z ) Condition z 9 InverseGammaRegularized a z -1 9 w w 1 -1 9 a 40320 w 8 -1 322560 a -1 w 7 144 a -1 7840 a -6361 w 6 -1 8 a -1 36 a 7840 a -11243 146221 w 5 4 a -1 a 180 a 3920 a -7323 829183 -175291 w 4 -1 8 a -1 2 a -1 4 a 45 a 784 a -1265 31337 -23411 w 3 2 a -1 2 a -1 a 4 a 45 a 1568 a -2619 75437 -87099 9511 w 2 -1 2 a a a 4 a a 36 a 1120 a -3403 152039 -101576 159365 -36893 4679 w 502 w a a a a 4 a a 36 a 280 a -761 29531 -16821 22449 -4536 546 -36 1 Gamma a 9 w InverseGammaRegularized a z [/itex]

 Rule Form

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

 2007-05-02