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; }

 InverseBetaRegularized

 http://functions.wolfram.com/06.23.06.0004.01

 Input Form

 InverseBetaRegularized[z, a, b] \[Proportional] w + ((b - 1)/(1 + a)) w^2 + (((-1 + b) (-4 + 5 b + a (-1 + a + 3 b)))/ (2 (1 + a)^2 (2 + a))) w^3 + (((-1 + b) (18 + a^4 + a^3 (-1 + 6 b) + a^2 (2 + b) (-5 + 8 b) + b (-47 + 31 b) + a (4 - 30 b + 33 b^2)))/(3 (1 + a)^3 (2 + a) (3 + a))) w^4 + (((-1 + b) (a (-632 + a (1016 + a (529 + a (-235 + a (-119 + a (11 + 6 a)))))) + a (4688 + a (-1636 + a (-2581 + a (-259 + a (269 + 55 a))))) b + 3 (-2104 + a (-3111 + a (-831 + a (637 + a (367 + 50 a))))) b^2 + (2888 + a (5661 + a (3971 + a (1179 + 125 a)))) b^3 + 8 (-144 + 581 b)))/(24 (1 + a)^4 (2 + a)^2 (3 + a) (4 + a))) w^5 + (((-1 + b) (2400 + a (684 + a (-3222 + a (-888 + a (1378 + a (379 + a (-203 + a (-57 + a (7 + 2 a)))))))) - 13196 b + a (-10248 + a (11715 + a (9810 + a (-2249 + a (-2612 + 5 a (-27 + a (34 + 5 a))))))) b + (27454 + a (35077 + a (-5120 + a (-20855 + a (-5564 + a (1993 + 15 a (66 + 7 a))))))) b^2 + 2 (-12818 + a (-22939 + a (-9970 + a (3650 + a (3978 + a (1049 + 90 a)))))) b^3 + (9074 + a (20997 + a (18375 + a (7575 + a (1471 + 108 a))))) b^4))/ (10 (1 + a)^5 (2 + a)^2 (3 + a) (4 + a) (5 + a))) w^6 + (((-1 + b) (a (-4936896 + a (10065072 + a (9049664 + a (-4942098 + a (-5856333 + a (388306 + a (1555497 + a (252156 + a (-140531 + a (-45078 + a (159 + 2 a (661 + 60 a)))))))))))) + a (56926752 + a (-37606016 + a (-77685178 + a (-6773219 + a (32310972 + a (12172733 + a (-3434538 + a (-2654803 + a (-283544 + a (104123 + 2 a (13968 + 959 a))))))))))) b + 5 (-24517200 + a (-44955776 + a (-4030870 + a (38501757 + a (22941654 + a (-4567008 + a (-7786674 + a (-1891930 + a (325642 + 3 a (75744 + a (12776 + 735 a))))))))))) b^2 + 5 (34873152 + a (82583314 + a (51845151 + a (-22412726 + a (-41061344 + a (-15228558 + a (1747434 + a (2877494 + a (870096 + a (115196 + 5831 a)))))))))) b^3 + 5 (-25045728 + a (-72983068 + a (-78195392 + a (-29625237 + a (10053702 + a (14698401 + a (6350196 + a (1395565 + a (157286 + 7203 a))))))))) b^4 + (36360816 + a (126276754 + a 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+ 672 a)))))))))))) b^3 + 5 (241888188 + a (632874386 + a (478191784 + a (-119971710 + a (-361456837 + a (-175887971 + a (-358935 + a (30300322 + a (12611711 + a (2423517 + 7 a (33199 + 1280 a))))))))))) b^4 + 3 (-236555412 + a (-754751926 + a (-910884912 + a (-435090718 + a (68351521 + a (189789789 + a (102900786 + a (29039428 + a (4653201 + a (400147 + 14336 a)))))))))) b^5 + (175331220 + a (662420842 + a (1069554738 + a (967463528 + a (539832153 + a (192606624 + a (43936962 + a (6181022 + a (486927 + 16384 a))))))))) b^6 - 432 (-44100 + 374917 b)))/(315 (1 + a)^7 (2 + a)^3 (3 + a)^2 (4 + a) (5 + a) (6 + a) (7 + a))) w^8 + (((-1 + b) (a (-13391437824 + a (44576037888 + a (39777942144 + a (-41076704064 + a (-46150895904 + a (13779022496 + a (26065842646 + a (1498242409 + a (-7135515526 + a (-2067637494 + a (728117266 + a (435172344 + a (24930050 + a (-25691102 + a (-6174816 + a (-197089 + 4 a (25051 + a (3453 + 140 a)))))))))))))))))) + a (229945657344 + a (-305774479616 + a 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a)^2 (4 + a)^2 (5 + a) (6 + a) (7 + a) (8 + a))) w^9 + (((-1 + b) (a (320899968000 + a (-1469876129280 + a (-1165993518240 + a (1738412530608 + a (1703029775000 + a (-897596215932 + a (-1269592245948 + a (93801596020 + a (500786446416 + a (100126221528 + a (-93464155906 + a (-42123596859 + a (3580326744 + a (5730579406 + a (993089874 + a (-168955152 + a (-83305942 + a (-9574386 + a (367620 + a (186103 + 18 a (919 + 28 a))))))))))))))))))))) + 2 a (-3399385708800 + a (6348442039488 + a (9956390624496 + a (-4043188991232 + a (-11213166021464 + a (-1137521480196 + a (5878948725435 + a (2421217082180 + a (-1251509376336 + a (-1037286954171 + a (-39938157440 + a (162435141633 + a (50034011493 + a (-3105877906 + a (-4569660237 + a (-891936810 + a (-9187262 + a (21978225 + a (3647586 + a (254213 + 6849 a)))))))))))))))))))) b + (27945269609472 + a (50569494562080 + a (-33642942036336 + a (-116066465941152 + a (-25985348388432 + a (90942075741590 + a (58901032905903 + a (-21981803591352 + a 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(-12885993451008 + a (-46004246797152 + a (-54621049672136 + a (-3977669713332 + a (49553472957270 + a (45065480843967 + a (7874944477119 + a (-12246352312569 + a (-9664461018083 + a (-2581867711554 + a (326502338718 + a (480937433610 + a (176677516512 + a (37125466299 + a (4924980139 + 9 a (45416299 + a (2159941 + 45000 a))))))))))))))))) b^5 + 14 (9682198814592 + a (40444333897848 + a (66039283849372 + a (44927776666926 + a (-6795617848539 + a (-35284629824571 + a (-26493465624255 + a (-7457711606907 + a (1918479329530 + a (2634297002646 + a (1189038960234 + a (323073734052 + a (58070902437 + a (6975061677 + a (539825449 + 3 a (8122723 + 162500 a)))))))))))))))) b^6 + 4 (-14686204963968 + a (-70440758773512 + a (-144324960690196 + a (-159973862320482 + a (-93686645350779 + a (-10189434004683 + a (29741210038620 + a (27820849055892 + a (13812363372194 + a (4529911782282 + a (1035984438060 + a (166644795390 + a (18508290993 + a (1351167633 + 4 a (14574029 + 281250 a))))))))))))))) b^7 + (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)))))))))))))) b^8 - 746496 (-635040 + 7346593 b)))/(4536 (1 + a)^9 (2 + a)^4 (3 + a)^3 (4 + a)^2 (5 + a) (6 + a) (7 + a) (8 + a) (9 + a))) w^10 + O[z^(11/a)] /; w == (a z Beta[a, b])^(1/a) && a > 0

 Standard Form

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

 2007-05-02