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variants of this functions
InverseBetaRegularized






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseBetaRegularized[z,a,b] > Differentiation > Low-order differentiation > With respect to z





http://functions.wolfram.com/06.23.20.0014.01









  


  










Input Form





D[InverseBetaRegularized[z, a, b], {z, 10}] == (1 - w)^(1 - 10 b) w^(1 - 10 a) (1 + 362880 a^9 (-1 + w)^9 + 144 a^8 (-1 + w)^8 (7129 + (-29809 + 22680 b) w) + w (-1022 + 1013 b + 12 (4665 - 9794 b + 5132 b^2) w + 2 (-409260 + b (1268531 + b (-1319488 + 460175 b))) w^2 + 2 (2551500 + b (-10136625 + b (15210663 + b (-10221181 + 2595706 b)))) w^3 + 6 (-2739240 + b (12978858 + b (-24732729 + b (23705985 + b (-11434409 + 2221514 b))))) w^4 + 2 (14817600 + b (-80250240 + b (181671791 + b (-220120778 + b (150610945 - 55199176 b + 8469900 b^2))))) w^5 + 4 (-7560000 + b (45530760 + b (-117628052 + b (169008835 + b (-145880941 + b (75659429 + 36 b (-606559 + 75169 b))))))) w^6 + 9 (-3 + 2 b) (-4 + 3 b) (-5 + 4 b) (-6 + 5 b) (-7 + 6 b) (-8 + 7 b) (-9 + 8 b) (-10 + 9 b) w^7 + (-2 + b) (-3 + 2 b) (-4 + 3 b) (-5 + 4 b) (-6 + 5 b) (-7 + 6 b) (-8 + 7 b) (-9 + 8 b) (-10 + 9 b) w^8) + 4 a^6 (-1 + w)^6 (180920 + w (-4035273 + 3492513 b + 12 (1388255 + 9 b (-252048 + 102823 b)) w + (-17039657 + 63 b (623583 + 16 b (-29809 + 7560 b))) w^2)) + a^5 (-1 + w)^5 (269325 + w (-11428952 + 10351652 b + 84088070 w + 8 b (-18194527 + 7885512 b) w + 12 (-16004050 + b (39251737 + 6 b (-5341167 + 1451590 b))) w^2 + 3 (44149747 + 4 b (-34079314 + 21 b (1870749 + 32 b (-29809 + 5670 b)))) w^3)) + a^4 (-1 + w)^4 (63273 + w (-5012192 + 4695827 b + 2 (29499368 + b (-53697485 + 24514482 b)) w + 10 (-22626598 + b (58687749 + 4 b (-12703961 + 3672855 b))) w^2 + 3 (112639183 + 4 b (-92161897 + 5 b (22592677 + 12 b (-1024245 + 208663 b)))) w^3 + 3 (-56964266 + 5 b (44149747 + 4 b (-17039657 + 21 b (623583 + 8 b (-29809 + 4536 b))))) w^4)) + 2 a^3 (-1 + w)^3 (4725 + w (-699529 + 671179 b + 9 (1386739 + 2 b (-1318625 + 629193 b)) w + (-71679082 + b (195619251 + b (-178611459 + 54576790 b))) w^2 + (173992430 + b (-600931908 + b (779370883 + 90 b (-4999408 + 1084291 b)))) w^3 + 6 (-31143509 + 2 b (63762462 + b (-104303544 + b (85198285 + 9 b (-3860985 + 629006 b))))) w^4 + (73222034 + b (-341785596 + b (662246205 + 2 b (-340793140 + 63 b (3117915 + 32 b (-29809 + 3780 b)))))) w^5)) + 36 a^7 (-1 + w)^7 (32575 + w (9 (-39498 + 69287 w) + 4 b (72583 + 8 (-29809 + 11340 b) w))) + a (-1 + w) (45 + w (-23918 + 910360 w + 3265920 b^8 w^7 - 144 b^7 w^6 (-165889 + 238472 w) + 36 b^6 w^5 (1728562 + 9 w (-633954 + 485009 w)) + 4 b^5 w^4 (18283872 + w (-107592458 + 3 (62986205 - 34079314 w) w)) - 2 b (-1 + 2 w) (11779 + 2 (-1 + w) w (452799 + 2 (-1 + w) w (3055390 + 10048977 (-1 + w) w))) + b^4 w^3 (40481788 + w (-397516538 + 3 w (414175476 + w (-514347352 + 220748735 w)))) + 6 w^2 (-1669717 + 2 w (3982529 + 20 w (-482555 + w (622787 + 3 w (-136073 + 35638 w))))) - 2 b^3 w^2 (-5012780 + 3 w (27874092 + w (-144711723 + 4 w (79849141 + w (-78648203 + 28482133 w))))) + 2 b^2 w (474606 + w (-14943243 + w (130381127 + 2 w (-238063322 + 3 w (138744960 + w (-115300559 + 36611017 w)))))))) + 2 a^2 (-1 + w)^2 (435 + w (-121399 + 6531840 b^7 w^6 - 504 b^6 w^5 (-75169 + 119236 w) + 162 b^5 w^4 (462805 + 3 w (-574376 + 485009 w)) - b^2 w (-1 + 2 w) (3118926 + (-1 + w) w (64434970 + 256339197 (-1 + w) w)) + 2 b^4 w^3 (31487069 - 5 w (43208773 - 85578882 w + 51118971 w^2)) + b^3 w^2 (22688575 + w (-274187543 + w (997920529 + 3 w (-465780764 + 220748735 w)))) + w (3188170 + w (-25808723 + w (90625419 - 2 w (77517068 + 9 w (-7073075 + 2233106 w))))) + b (118354 + w (-6297961 + w (73777745 + 2 w (-164520448 + 3 w (111407420 + w (-104365543 + 36611017 w))))))))) Beta[a, b]^10 /; w == InverseBetaRegularized[z, a, b]










Standard Form





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- </mo> <mn> 22626598 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 24514482 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 53697485 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 29499368 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mrow> <mn> 4695827 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5012192 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 63273 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 63 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 32 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3780 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 29809 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3117915 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 340793140 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 662246205 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 341785596 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 73222034 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 629006 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3860985 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 85198285 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 104303544 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 63762462 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 31143509 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 90 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1084291 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4999408 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 779370883 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 600931908 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 173992430 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 54576790 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 178611459 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 195619251 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 71679082 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 629193 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 1318625 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1386739 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mrow> <mn> 671179 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 699529 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4725 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6531840 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 504 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 119236 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 75169 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 162 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 485009 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 574376 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 462805 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 31487069 </mn> <mo> - </mo> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 51118971 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 85578882 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 43208773 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> w </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 220748735 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 465780764 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 997920529 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 274187543 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 22688575 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 256339197 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 64434970 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3118926 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 36611017 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 104365543 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 111407420 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 164520448 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 73777745 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 6297961 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 118354 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 90625419 </mn> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2233106 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 7073075 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 77517068 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 25808723 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3188170 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 121399 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 435 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3265920 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 7 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 144 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 238472 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 165889 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 485009 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 633954 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1728562 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 62986205 </mn> <mo> - </mo> <mrow> <mn> 34079314 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 107592458 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 18283872 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> w </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 220748735 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 514347352 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 414175476 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 397516538 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 40481788 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 28482133 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 78648203 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 79849141 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 144711723 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 27874092 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 5012780 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 36611017 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 115300559 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 138744960 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 238063322 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 130381127 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 14943243 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 474606 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 10048977 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mn> 3055390 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 452799 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 11779 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 910360 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 35638 </mn> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> - </mo> <mn> 136073 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 622787 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 482555 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 3982529 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 1669717 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 23918 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> w </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 7 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 9 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 10 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 36 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 75169 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 606559 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 75659429 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 145880941 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 169008835 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 117628052 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 45530760 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 7560000 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8469900 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 55199176 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 150610945 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 220120778 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 181671791 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 80250240 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 14817600 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2221514 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 11434409 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 23705985 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 24732729 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 12978858 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2739240 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2595706 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 10221181 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 15210663 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 10136625 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2551500 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 460175 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 1319488 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1268531 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 409260 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5132 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 9794 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 4665 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> w </mi> </mrow> <mo> + </mo> <mrow> <mn> 1013 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mn> 1022 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <semantics> <mi> &#914; </mi> <annotation-xml encoding='MathML-Content'> <ci> Beta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> 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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.