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/06.12.06.0007.01

 Input Form

 InverseGammaRegularized[a, z] \[Proportional] w + (1/(a + 1)) w^2 + ((3 a + 5)/(2 (a + 1)^2 (a + 2))) w^3 + ((31 + a (33 + 8 a))/(3 (1 + a)^3 (2 + a) (3 + a))) w^4 + ((2888 + a (5661 + a (3971 + a (1179 + 125 a))))/ (24 (1 + a)^4 (2 + a)^2 (3 + a) (4 + a))) w^5 + ((9074 + a (20997 + a (18375 + a (7575 + a (1471 + 108 a)))))/ (10 (1 + a)^5 (2 + a)^2 (3 + a) (4 + a) (5 + a))) w^6 + (1/(720 (1 + a)^6 (2 + a)^3 (3 + a)^2 (4 + a) (5 + a) (6 + a))) (36360816 + a (126276754 + a (185250179 + a (149847504 + a (73069137 + a (21989226 + a (3987861 + a (398516 + 16807 a)))))))) w^7 + (1/(315 (1 + a)^7 (2 + a)^3 (3 + a)^2 (4 + a) (5 + a) (6 + a) (7 + a))) (175331220 + a (662420842 + a (1069554738 + a (967463528 + a (539832153 + a (192606624 + a (43936962 + a (6181022 + a (486927 + 16384 a))))))))) w^8 + (1/(4480 (1 + a)^8 (2 + a)^4 (3 + a)^2 (4 + a)^2 (5 + a) (6 + a) (7 + a) (8 + a))) (254843639808 + a (1227828808512 + a (2628223795120 + a (3302979236810 + a (2712896385015 + a (1533600689586 + a (611682241930 + a (173423227630 + a (34688913336 + a (4774846502 + a (429446950 + a (22669360 + 531441 a)))))))))))) w^9 + (1/(4536 (1 + a)^9 (2 + a)^4 (3 + a)^3 (4 + a)^2 (5 + a) (6 + a) (7 + a) (8 + a) (9 + a))) (11250058301568 + a (61077979985160 + a (149504225861948 + a (218591764868766 + a (213209054640489 + a (146718794936892 + a (73445003464698 + a (27165941822238 + a (7460377417652 + a (1513727910042 + a (223389222954 + a (23253261756 + a (1614236211 + 2 a (33456213 + 625000 a)))))))))))))) w^10 + O[(z - 1)^(11/a)] /; w == ((-(z - 1)) Gamma[a + 1])^(1/a)

 Standard Form

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 MathML Form

 Q GammaRegularized - 1 ( a , z ) w + w 2 a + 1 + ( 3 a + 5 ) w 3 2 ( a + 1 ) 2 ( a + 2 ) + ( a ( 8 a + 33 ) + 31 ) w 4 3 ( a + 1 ) 3 ( a + 2 ) ( a + 3 ) + ( a ( a ( a ( 125 a + 1179 ) + 3971 ) + 5661 ) + 2888 ) w 5 24 ( a + 1 ) 4 ( a + 2 ) 2 ( a + 3 ) ( a + 4 ) + ( a ( a ( a ( a ( 108 a + 1471 ) + 7575 ) + 18375 ) + 20997 ) + 9074 ) w 6 10 ( a + 1 ) 5 ( a + 2 ) 2 ( a + 3 ) ( a + 4 ) ( a + 5 ) + 1 720 ( a + 1 ) 6 ( a + 2 ) 3 ( a + 3 ) 2 ( a + 4 ) ( a + 5 ) ( a + 6 ) ( a ( a ( a ( a ( a ( a ( a ( 16807 a + 398516 ) + 3987861 ) + 21989226 ) + 73069137 ) + 149847504 ) + 185250179 ) + 126276754 ) + 36360816 ) w 7 + 1 315 ( a + 1 ) 7 ( a + 2 ) 3 ( a + 3 ) 2 ( a + 4 ) ( a + 5 ) ( a + 6 ) ( a + 7 ) ( a ( a ( a ( a ( a ( a ( a ( a ( 16384 a + 486927 ) + 6181022 ) + 43936962 ) + 192606624 ) + 539832153 ) + 967463528 ) + 1069554738 ) + 662420842 ) + 175331220 ) w 8 + 1 4480 ( a + 1 ) 8 ( a + 2 ) 4 ( a + 3 ) 2 ( a + 4 ) 2 ( a + 5 ) ( a + 6 ) ( a + 7 ) ( a + 8 ) ( a ( a ( a ( a ( a ( a ( a ( a ( a ( a ( a ( 531441 a + 22669360 ) + 429446950 ) + 4774846502 ) + 34688913336 ) + 173423227630 ) + 611682241930 ) + 1533600689586 ) + 2712896385015 ) + 3302979236810 ) + 2628223795120 ) + 1227828808512 ) + 254843639808 ) w 9 + 1 4536 ( a + 1 ) 9 ( a + 2 ) 4 ( a + 3 ) 3 ( a + 4 ) 2 ( a + 5 ) ( a + 6 ) ( a + 7 ) ( a + 8 ) ( a + 9 ) ( a ( a ( a ( a ( a ( a ( a ( a ( a ( a ( a ( a ( 2 a ( 625000 a + 33456213 ) + 1614236211 ) + 23253261756 ) + 223389222954 ) + 1513727910042 ) + 7460377417652 ) + 27165941822238 ) + 73445003464698 ) + 146718794936892 ) + 213209054640489 ) + 218591764868766 ) + 149504225861948 ) + 61077979985160 ) + 11250058301568 ) w 10 + O ( ( z - 1 ) 11 / a ) /; w ( - ( z - 1 ) Γ ( a + 1 ) ) 1 / a Condition Proportional InverseGammaRegularized a z w w 2 a 1 -1 3 a 5 w 3 2 a 1 2 a 2 -1 a 8 a 33 31 w 4 3 a 1 3 a 2 a 3 -1 a a a 125 a 1179 3971 5661 2888 w 5 24 a 1 4 a 2 2 a 3 a 4 -1 a a a a 108 a 1471 7575 18375 20997 9074 w 6 10 a 1 5 a 2 2 a 3 a 4 a 5 -1 1 720 a 1 6 a 2 3 a 3 2 a 4 a 5 a 6 -1 a a a a a a a 16807 a 398516 3987861 21989226 73069137 149847504 185250179 126276754 36360816 w 7 1 315 a 1 7 a 2 3 a 3 2 a 4 a 5 a 6 a 7 -1 a a a a a a a a 16384 a 486927 6181022 43936962 192606624 539832153 967463528 1069554738 662420842 175331220 w 8 1 4480 a 1 8 a 2 4 a 3 2 a 4 2 a 5 a 6 a 7 a 8 -1 a a a a a a a a a a a 531441 a 22669360 429446950 4774846502 34688913336 173423227630 611682241930 1533600689586 2712896385015 3302979236810 2628223795120 1227828808512 254843639808 w 9 1 4536 a 1 9 a 2 4 a 3 3 a 4 2 a 5 a 6 a 7 a 8 a 9 -1 a a a a a a a a a a a a 2 a 625000 a 33456213 1614236211 23253261756 223389222954 1513727910042 7460377417652 27165941822238 73445003464698 146718794936892 213209054640489 218591764868766 149504225861948 61077979985160 11250058301568 w 10 O z -1 11 a -1 w -1 z -1 Gamma a 1 1 a -1 [/itex]

 Rule Form

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

 2007-05-02

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