l2.txt

This file contains the explicit expressions necessary for the case (l,m)=(l,l), l >= 4.

A=(-12+3 l^2+12 n^2+4 x+x^2+8 n (1+x)+4 l (1+3 n+x))/(4 (1+n) (3+2 l+2 n))

B=-(((-4+l+2 n+x) (2+l+2 n+x))/(4 (1+n) (3+2 l+2 n)))

n0=2

r_2=(-3360 l-1440 l^2+1944 l^3+1524 l^4+360 l^5+27 l^6-4192 x-3104 l x+4440 l^2 x+4424 l^3 x+1236 l^4 x+108 l^5 x-1536 x^2+3432 l x^2+4704 l^2 x^2+1632 l^3 x^2+171 l^4 x^2+936 x^3+2168 l x^3+1032 l^2 x^3+136 l^3 x^3+364 x^4+312 l x^4+57 l^2 x^4+36 x^5+12 l x^5+x^6)/(12 (7+2 l) (-120 l+24 l^2+52 l^3+9 l^4-136 x+56 l x+112 l^2 x+24 l^3 x+32 x^2+76 l x^2+22 l^2 x^2+16 x^3+8 l x^3+x^4))

rtilde=(4+n)/(6+n)+(3 (-2+l))/(8+8 n)+((1+l+2 n) x)/(3+5 n+2 n^2+l (2+2 n))+x^2/(12+20 n+8 n^2+l (8+8 n))

a=(3960+5880 l-4050 l^2+60 l^3+10044 n-732 l n-1629 l^2 n+222 l^3 n+4084 n^2-2084 l n^2+281 l^2 n^2-58 l^3 n^2-608 n^3-472 l n^3-68 l^2 n^3-20 l^3 n^3-512 n^4+72 l n^4-68 l^2 n^4+96 n^5-48 l n^5+5280 x-5360 l x+80 l^2 x-7664 n x-2392 l n x-344 l^2 n x-6064 n^2 x-104 l n^2 x-312 l^2 n^2 x+416 n^3 x-448 l n^3 x-48 l^2 n^3 x+256 n^4 x-96 l n^4 x-1320 x^2+20 l x^2-964 n x^2-566 l n x^2-500 n^2 x^2-254 l n^2 x^2-152 n^3 x^2-28 l n^3 x^2-16 n^4 x^2)/((-30-45 l+30 l^2-42 n+69 l n+6 l^2 n+44 n^2+22 l n^2+16 n^3-40 x+40 l x+72 n x+8 l n x+16 n^2 x+10 x^2+2 n x^2) (-12+46 l+36 l^2+94 n+113 l n+6 l^2 n+92 n^2+22 l n^2+16 n^3+48 x+48 l x+104 n x+8 l n x+16 n^2 x+12 x^2+2 n x^2))

b=(16 n (5+n) (6+n) (1+2 l+2 n) (-4+l+2 n+x) (2+l+2 n+x))/((-30-45 l+30 l^2-42 n+69 l n+6 l^2 n+44 n^2+22 l n^2+16 n^3-40 x+40 l x+72 n x+8 l n x+16 n^2 x+10 x^2+2 n x^2) (-12+46 l+36 l^2+94 n+113 l n+6 l^2 n+92 n^2+22 l n^2+16 n^3+48 x+48 l x+104 n x+8 l n x+16 n^2 x+12 x^2+2 n x^2))

esta=-(13+2 l+2 n)^2 (507177216+477813792 l+150566400 l^2+21172920 l^3+894096 l^4+670863336 n+507990708 l n+118663614 l^2 n+10130739 l^3 n+239490 l^4 n+355501704 n^2+200419844 l n^2+30318790 l^2 n^2+1366095 l^3 n^2+15966 l^4 n^2+97780880 n^3+37572616 l n^3+2876764 l^2 n^3+48894 l^3 n^3+16118784 n^4+3289792 l n^4+48160 l^2 n^4+1569024 n^5+80768 l n^5+65536 n^6) (731015424+678496800 l+193443072 l^2+20484792 l^3+894096 l^4+986282856 n+715038516 l n+151633182 l^2 n+11666739 l^3 n+239490 l^4 n+560865288 n^2+313406084 l n^2+49302694 l^2 n^2+2459727 l^3 n^2+15966 l^4 n^2+169944464 n^3+69590536 l n^3+7555612 l^2 n^3+171774 l^3 n^3+27409920 n^4+7804864 l n^4+465952 l^2 n^4+2158848 n^5+375680 l n^5+65536 n^6)-16 (183380052049938432+369796139532651264 l+303054058457392768 l^2+130953976072386368 l^3+32713930304613600 l^4+4918586642430848 l^5+441724675590208 l^6+21779243931648 l^7+444115365120 l^8+479731790357101248 n+868578006118285696 l n+621319534114252576 l^2 n+229382057600898816 l^3 n+48511034516992652 l^4 n+6097408618370600 l^5 n+445988242716480 l^6 n+17003572606944 l^7 n+237918945600 l^8 n+593634968074498240 n^2+938246371871817584 l n^2+572114374996308272 l^2 n^2+177262423434661304 l^3 n^2+31081358994314476 l^4 n^2+3183139374107755 l^5 n^2+184072453374207 l^6 n^2+5239432565436 l^7 n^2+47725407540 l^8 n^2+456270358595899296 n^3+612270994484543504 l n^3+311627008739122064 l^2 n^3+79424650510446168 l^3 n^3+11226817995394330 l^4 n^3+903527658264825 l^5 n^3+39692692203730 l^6 n^3+797921467428 l^7 n^3+4248552600 l^8 n^3+239072170008102720 n^4+266429741353114832 l n^4+111115493597357104 l^2 n^4+22700601648255624 l^3 n^4+2481264538837780 l^4 n^4+148862268506081 l^5 n^4+4687177319515 l^6 n^4+60141548388 l^7 n^4+141618420 l^8 n^4+88458316273129632 n^5+80672448385385136 l n^5+27058988444555312 l^2 n^5+4267484399734312 l^3 n^5+338111066661834 l^4 n^5+13952647878395 l^5 n^5+284606312600 l^6 n^5+1796824284 l^7 n^5+23361465333262208 n^6+17276163351586112 l n^6+4548291173655808 l^2 n^6+521933588224928 l^3 n^6+26948548437912 l^4 n^6+665289554724 l^5 n^6+6840280316 l^6 n^6+4393939508224896 n^7+2614649202034240 l n^7+519485791221696 l^2 n^7+39304934726304 l^3 n^7+1084159476056 l^4 n^7+11521965620 l^5 n^7+581005952553472 n^8+274584256927744 l n^8+38385044067072 l^2 n^8+1600039626240 l^3 n^8+14255896608 l^4 n^8+52561395066880 n^9+19116945118208 l n^9+1642727849472 l^2 n^9+24994252544 l^3 n^9+3088257933312 n^10+796248940544 l n^10+30507505664 l^2 n^10+105977479168 n^11+15042871296 l n^11+1610612736 n^12) t^2-8 (6245486716871168+10207281990151168 l+6395617438262656 l^2+1939946418572416 l^3+297926394339520 l^4+21814982339584 l^5+582284589824 l^6+11201519879864704 n+16864483782557632 l n+9329329893478624 l^2 n+2380903445976976 l^3 n+300437516072304 l^4 n+17354410910144 l^5 n+311938173120 l^6 n+8535749435325808 n^2+11941296993153440 l n^2+5719666914517784 l^2 n^2+1197376735356248 l^3 n^2+120254706168259 l^4 n^2+5353696859848 l^5 n^2+62573312108 l^6 n^2+3620703950834720 n^3+4744650096626048 l n^3+1912733980171760 l^2 n^3+317245725656704 l^3 n^3+24426910546338 l^4 n^3+806998723848 l^5 n^3+5570324520 l^6 n^3+946106096508080 n^4+1160951658575328 l n^4+377561447103512 l^2 n^4+47095182413768 l^3 n^4+2644420667823 l^4 n^4+59743416664 l^5 n^4+185677484 l^6 n^4+160372700989824 n^5+179812953756608 l n^5+44074212067808 l^2 n^5+3796557591280 l^3 n^5+143083007184 l^4 n^5+1743834904 l^5 n^5+18271806059712 n^6+17299277839488 l n^6+2823201128096 l^2 n^6+142032581536 l^3 n^6+2946375084 l^4 n^6+1451972836864 n^7+954189351680 l n^7+76976070272 l^2 n^7+1343743552 l^3 n^7+83221851136 n^8+23992210432 l n^8+33030912 l^2 n^8+3296198656 n^9+72613888 l n^9+67108864 n^10) t^4-64 (7+n) (8+n) (1762+887 l+512 n)^2 (20908+4832 l+280 l^2+16200 n+2551 l n+75 l^2 n+4562 n^2+412 l n^2+5 l^2 n^2+550 n^3+21 l n^3+24 n^4) t^6-16 (7+n)^2 (8+n)^2 (1762+887 l+512 n)^2 t^8

estb=-(13+2 l+2 n)^2 (631717120+661634976 l+239851968 l^2+38524216 l^3+2087568 l^4+913078216 n+641541268 l n+176021078 l^2 n+19339139 l^3 n+559170 l^4 n+437937320 n^2+219072804 l n^2+47886702 l^2 n^2+3375071 l^3 n^2+37278 l^4 n^2+87689232 n^3+36552456 l n^3+6277308 l^2 n^3+196894 l^3 n^3+7171200 n^4+3535808 l n^4+335104 l^2 n^4+171776 n^5+175488 l n^5) (2208677120+2016386976 l+560261568 l^2+58594616 l^3+2087568 l^4+4030646216 n+2682450068 l n+522401878 l^2 n+34750339 l^3 n+559170 l^4 n+2861028520 n^2+1353626404 l n^2+173576302 l^2 n^2+6421471 l^3 n^2+37278 l^4 n^2+1024060432 n^3+323822856 l n^3+24370108 l^2 n^3+376094 l^3 n^3+195075200 n^4+36841408 l n^4+1231104 l^2 n^4+18782976 n^5+1609088 l n^5+716800 n^6)-16 (1064709492046956544+2089568412408369920 l+1674142523882237568 l^2+714605457755504960 l^3+178595183193441504 l^4+26972498234730368 l^5+2421086942746688 l^6+118560412895232 l^7+2421077863680 l^8+3603280198200206528 n+5960414047033397376 l n+4013566718381697184 l^2 n+1438650238981620288 l^3 n+299876495071963916 l^4 n+37112111388062760 l^5 n+2639509284202816 l^6 n+96355755097056 l^7 n+1297005998400 l^8 n+5323961090334216384 n^2+7410375236098164720 l n^2+4186552333785939056 l^2 n^2+1251286136392295128 l^3 n^2+214660056525572828 l^4 n^2+21337577220334843 l^5 n^2+1168590208266239 l^6 n^2+30554261254524 l^7 n^2+260173227060 l^8 n^2+4567722334167338656 n^3+5337701109041430800 l n^3+2515580470188293008 l^2 n^3+619819380462141208 l^3 n^3+85913419850333098 l^4 n^3+6672935798382457 l^5 n^3+270122376001682 l^6 n^3+4751380839972 l^7 n^3+23160821400 l^8 n^3+2550403981318565184 n^4+2489045409394760784 l n^4+968597652820577008 l^2 n^4+193432442546158312 l^3 n^4+21101145584452932 l^4 n^4+1229850110792817 l^5 n^4+34478971002459 l^6 n^4+363694630692 l^7 n^4+772027380 l^8 n^4+981711660479361952 n^5+792612552343218864 l n^5+250661547655205808 l^2 n^5+39567173823588264 l^3 n^5+3265573431399738 l^4 n^5+133858758593179 l^5 n^5+2308716854616 l^6 n^5+10991617116 l^7 n^5+268334545577918848 n^6+176537662850110784 l n^6+44290048855143424 l^2 n^6+5318138756810400 l^3 n^6+311528886293816 l^4 n^6+7976029237092 l^5 n^6+63454870908 l^6 n^6+52667884023187328 n^7+27583861294181952 l n^7+5288467158507968 l^2 n^7+453669520718496 l^3 n^7+16765262741656 l^4 n^7+200840522932 l^5 n^7+7388431167736320 n^8+2969738777890816 l n^8+409063764491008 l^2 n^8+22308674681856 l^3 n^8+389801871008 l^4 n^8+724009199560704 n^9+210146684736512 l n^9+18526328937984 l^2 n^9+481936989952 l^3 n^9+47115488649216 n^10+8805216034816 l n^10+373214255104 l^2 n^10+1830145228800 n^11+165586534400 l n^11+32112640000 n^12) t^2-8 (49891003222872576+76765160329761792 l+44238396850582912 l^2+12130077242937472 l^3+1708255375200448 l^4+118702879669248 l^5+3174302087936 l^6+148310253654873472 n+184097734938159040 l n+83963545646682592 l^2 n+18103840483952784 l^3 n+1960702566782320 l^4 n+99407448749504 l^5 n+1700518975680 l^6 n+187147985579170800 n^2+185502979868153952 l n^2+66563246968935672 l^2 n^2+11081240921693160 l^3 n^2+894707365559555 l^4 n^2+31796807350536 l^5 n^2+341116008812 l^6 n^2+132575551368240160 n^3+103932913336847488 l n^3+28907076032030960 l^2 n^3+3616438748832576 l^3 n^3+208922620951970 l^4 n^3+4925789516808 l^5 n^3+30366410280 l^6 n^3+58747420057742128 n^4+35881500569987744 l n^4+7545256154178552 l^2 n^4+681656133181144 l^3 n^4+26509499025391 l^4 n^4+372672987288 l^5 n^4+1012213676 l^6 n^4+17107517025916544 n^5+7946491394568256 l n^5+1215368389530784 l^2 n^5+74487287510480 l^3 n^5+1743373592400 l^4 n^5+11074929304 l^5 n^5+3329541016785600 n^6+1132293146564480 l n^6+118308424534816 l^2 n^6+4386735807456 l^3 n^6+46647981484 l^4 n^6+429065647059456 n^7+100360436555008 l n^7+6381823020416 l^2 n^7+107814653888 l^3 n^7+35134086224896 n^8+5033449296896 l n^8+146477332224 l^2 n^8+1654801612800 n^9+109095526400 l n^9+34119680000 n^10) t^4-64 (7+n) (8+n) (4042+2071 l+2800 n)^2 (20908+4832 l+280 l^2+16200 n+2551 l n+75 l^2 n+4562 n^2+412 l n^2+5 l^2 n^2+550 n^3+21 l n^3+24 n^4) t^6-16 (7+n)^2 (8+n)^2 (4042+2071 l+2800 n)^2 t^8

esterror=-35133353164800-80162347991040 l-82277048779776 l^2-50250996868608 l^3-20349300057408 l^4-5759373921408 l^5-1169047136448 l^6-171631296144 l^7-18107258976 l^8-1340342136 l^9-66153501 l^10-1956636 l^11-26244 l^12+(-5296727330816-9538144195584 l-7570881891648 l^2-3492691841152 l^3-1038632551936 l^4-208337531232 l^5-28586264480 l^6-2652332536 l^7-159388100 l^8-5603580 l^9-87480 l^10) t^2+(-286063282176-373039659776 l-211245392960 l^2-67666012112 l^3-13394607712 l^4-1677135064 l^5-129646078 l^6-5649624 l^7-105948 l^8) t^4+(-5861331200-5096425728 l-1865799776 l^2-365568168 l^3-40168772 l^4-2331576 l^5-55440 l^6) t^6+(-35995968-19002960 l-3824397 l^2-345420 l^3-11772 l^4) t^8+(-67104-16524 l-1080 l^2) t^10-36 t^12