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variants of this functions
InverseGammaRegularized






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseGammaRegularized[a,z] > Series representations > Generalized power series > Expansions at z==1





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







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Rule Form





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





2007-05-02





© 1998-2014 Wolfram Research, Inc.