Rule: Q[1, 80, 82]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{81}-40\cdot t^{79}+\frac{3081}{8}\cdot t^{77}-\frac{19019}{8}\cdot t^{75}+\frac{1353275}{128}\cdot t^{73}-\frac{2309355}{64}\cdot t^{71}+\frac{100679775}{1024}\cdot t^{69}-\frac{224947383}{1024}\cdot t^{67}+\frac{13442126049}{32768}\cdot t^{65}-\frac{1329890705}{2048}\cdot t^{63}+\frac{57717256597}{65536}\cdot t^{61}-\frac{67620089355}{65536}\cdot t^{59}+\frac{1101885456061}{1048576}\cdot t^{57}-\frac{490136339987}{524288}\cdot t^{55}+\frac{6116407267905}{8388608}\cdot t^{53}-\frac{4193238415509}{8388608}\cdot t^{51}+\frac{162011484235575}{536870912}\cdot t^{49}-\frac{21552658988805}{134217728}\cdot t^{47}+\frac{2588713818544245}{34359738368}\cdot t^{45}-\frac{1070520752029575}{34359738368}\cdot t^{43}+\frac{6236646703759395}{549755813888}\cdot t^{41}-\frac{998058215667975}{274877906944}\cdot t^{39}+\frac{4482188713999815}{4398046511104}\cdot t^{37}-\frac{1099903346913735}{4398046511104}\cdot t^{35}+\frac{7522327487513475}{140737488355328}\cdot t^{33}-\frac{174201268131891}{17592186044416}\cdot t^{31}+\frac{890149337157465}{562949953421312}\cdot t^{29}-\frac{121683714103007}{562949953421312}\cdot t^{27}+\frac{225984040477013}{9007199254740992}\cdot t^{25}-\frac{11027197811175}{4503599627370496}\cdot t^{23}+\frac{14307082288345}{72057594037927936}\cdot t^{21}-\frac{950185730725}{72057594037927936}\cdot t^{19}+\frac{6499270398159}{9223372036854775808}\cdot t^{17}-\frac{68328754959}{2305843009213693952}\cdot t^{15}+\frac{140676848445}{147573952589676412928}\cdot t^{13}-\frac{3335195799}{147573952589676412928}\cdot t^{11}+\frac{886163135}{2361183241434822606848}\cdot t^9-\frac{4790071}{1180591620717411303424}\cdot t^7+\frac{481299}{18889465931478580854784}\cdot t^5-\frac{1435}{18889465931478580854784}\cdot t^3+\frac{41}{604462909807314587353088}\cdot t$
• $P_3$:
  $2\cdot t^{163}-81\cdot t^{161}+1610\cdot t^{159}-20935\cdot t^{157}+\frac{25637001}{128}\cdot t^{155}-\frac{384877493}{256}\cdot t^{153}+\frac{4720839123}{512}\cdot t^{151}-\frac{48647409525}{1024}\cdot t^{149}+\frac{6876747915675}{32768}\cdot t^{147}-\frac{52899198482515}{65536}\cdot t^{145}+\frac{179307672778395}{65536}\cdot t^{143}-\frac{1081705764538945}{131072}\cdot t^{141}+\frac{93652946456134975}{4194304}\cdot t^{139}-\frac{457577895802746075}{8388608}\cdot t^{137}+\frac{2029902703475420207}{16777216}\cdot t^{135}-\frac{8214975370440794529}{33554432}\cdot t^{133}+\frac{974473700023368842913}{2147483648}\cdot t^{131}-\frac{3320385576510198358305}{4294967296}\cdot t^{129}+\frac{651947852922093741585}{536870912}\cdot t^{127}-\frac{1893370152896432677467}{1073741824}\cdot t^{125}+\frac{163040207610526147226325}{68719476736}\cdot t^{123}-\frac{407356203030894999213825}{137438953472}\cdot t^{121}+\frac{946672866198558800989875}{274877906944}\cdot t^{119}-\frac{2049519023613962794249125}{549755813888}\cdot t^{117}+\frac{66228743305925483437021725}{17592186044416}\cdot t^{115}-\frac{124929327300817710483360405}{35184372088832}\cdot t^{113}+\frac{110166218389015394640287715}{35184372088832}\cdot t^{111}-\frac{181823401801821839491472425}{70368744177664}\cdot t^{109}+\frac{4496691357166064484230280225}{2251799813685248}\cdot t^{107}-\frac{6513598131925607072814794165}{4503599627370496}\cdot t^{105}+\frac{8846827313510899158599198045}{9007199254740992}\cdot t^{103}-\frac{11271497423689729148707636995}{18014398509481984}\cdot t^{101}+\frac{862440333176259578802629800375}{2305843009213693952}\cdot t^{99}-\frac{967776557075650061709821226375}{4611686018427387904}\cdot t^{97}+\frac{254862423628067120323581879525}{2305843009213693952}\cdot t^{95}-\frac{252040026910148326078580972775}{4611686018427387904}\cdot t^{93}+\frac{59901513062311918831342744529525}{2361183241434822606848}\cdot t^{91}-\frac{52201893166666803067535334932625}{4722366482869645213696}\cdot t^{89}+\frac{42694781462127652634183035003375}{9444732965739290427392}\cdot t^{87}-\frac{32763318451245035590662304399513}{18889465931478580854784}\cdot t^{85}+\frac{377306602809499280834401376471811}{604462909807314587353088}\cdot t^{83}-\frac{254605268562507644790693611765531}{1208925819614629174706176}\cdot t^{81}+\frac{80495810903837311584879713321655}{1208925819614629174706176}\cdot t^{79}-\frac{47666268190413753025757139485685}{2417851639229258349412352}\cdot t^{77}+\frac{422640911288335276828379970106407}{77371252455336267181195264}\cdot t^{75}-\frac{219015598286672342334034438290435}{154742504910672534362390528}\cdot t^{73}+\frac{106037765714328466406382185671935}{309485009821345068724781056}\cdot t^{71}-\frac{47918502964194624298937939879025}{618970019642690137449562112}\cdot t^{69}+\frac{646073608931037865547749465265475}{39614081257132168796771975168}\cdot t^{67}-\frac{253499334400448042719800189476835}{79228162514264337593543950336}\cdot t^{65}+\frac{11563127534055524755640008642803}{19807040628566084398385987584}\cdot t^{63}-\frac{3918582001389977415888415214193}{39614081257132168796771975168}\cdot t^{61}+\frac{39401126717272849841075823307545}{2535301200456458802993406410752}\cdot t^{59}-\frac{11459345200281122909753651823765}{5070602400912917605986812821504}\cdot t^{57}+\frac{3078975579065433024236839782951}{10141204801825835211973625643008}\cdot t^{55}-\frac{762682024172171483067841047153}{20282409603651670423947251286016}\cdot t^{53}+\frac{2780359336796963766316097785653}{649037107316853453566312041152512}\cdot t^{51}-\frac{581235965636354943769966334925}{1298074214633706907132624082305024}\cdot t^{49}+\frac{55589906928135443548591445175}{1298074214633706907132624082305024}\cdot t^{47}-\frac{9700191991818307421473341765}{2596148429267413814265248164610048}\cdot t^{45}+\frac{24623564286923395762201559865}{83076749736557242056487941267521536}\cdot t^{43}-\frac{3538927033438138846612765965}{166153499473114484112975882535043072}\cdot t^{41}+\frac{458874156770916169231889325}{332306998946228968225951765070086144}\cdot t^{39}-\frac{53437961679592783498480275}{664613997892457936451903530140172288}\cdot t^{37}+\frac{711793649572175876199757263}{170141183460469231731687303715884105728}\cdot t^{35}-\frac{65814642035034133075191231}{340282366920938463463374607431768211456}\cdot t^{33}+\frac{1343155959898655777044719}{170141183460469231731687303715884105728}\cdot t^{31}-\frac{96102095915198482278165}{340282366920938463463374607431768211456}\cdot t^{29}+\frac{382524028838927292205245}{43556142965880123323311949751266331066368}\cdot t^{27}-\frac{20482980033937983152409}{87112285931760246646623899502532662132736}\cdot t^{25}+\frac{933874469632430842815}{174224571863520493293247799005065324265472}\cdot t^{23}-\frac{35782256673785401065}{348449143727040986586495598010130648530944}\cdot t^{21}+\frac{18150420051920130975}{11150372599265311570767859136324180752990208}\cdot t^{19}-\frac{467216894306539575}{22300745198530623141535718272648361505980416}\cdot t^{17}+\frac{4770382704631335}{22300745198530623141535718272648361505980416}\cdot t^{15}-\frac{75039727938021}{44601490397061246283071436545296723011960832}\cdot t^{13}+\frac{14002628658291}{1427247692705959881058285969449495136382746624}\cdot t^{11}-\frac{114964110495}{2854495385411919762116571938898990272765493248}\cdot t^9+\frac{616980915}{5708990770823839524233143877797980545530986496}\cdot t^7-\frac{1929501}{11417981541647679048466287755595961091061972992}\cdot t^5+\frac{91881}{730750818665451459101842416358141509827966271488}\cdot t^3-\frac{41}{1461501637330902918203684832716283019655932542976}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.