Rule: Q[1, 86, 88]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{87}-43\cdot t^{85}+\frac{1785}{4}\cdot t^{83}-\frac{23821}{8}\cdot t^{81}+\frac{459405}{32}\cdot t^{79}-\frac{3410667}{64}\cdot t^{77}+\frac{40567527}{256}\cdot t^{75}-\frac{198544775}{512}\cdot t^{73}+\frac{26088783435}{32768}\cdot t^{71}-\frac{91182316225}{65536}\cdot t^{69}+\frac{548496702215}{262144}\cdot t^{67}-\frac{1431790092795}{524288}\cdot t^{65}+\frac{1632743088275}{524288}\cdot t^{63}-\frac{3270510001437}{1048576}\cdot t^{61}+\frac{11554118344845}{4194304}\cdot t^{59}-\frac{18053969395461}{8388608}\cdot t^{57}+\frac{800392643198771}{536870912}\cdot t^{55}-\frac{984741570132705}{1073741824}\cdot t^{53}+\frac{2153926799433123}{4294967296}\cdot t^{51}-\frac{2094780068098575}{8589934592}\cdot t^{49}+\frac{3622737294241065}{34359738368}\cdot t^{47}-\frac{2783353955276895}{68719476736}\cdot t^{45}+\frac{3795482666286675}{274877906944}\cdot t^{43}-\frac{2292522306124995}{549755813888}\cdot t^{41}+\frac{156655690918541325}{140737488355328}\cdot t^{39}-\frac{73702772679770871}{281474976710656}\cdot t^{37}+\frac{60900802239115881}{1125899906842624}\cdot t^{35}-\frac{22001200566043685}{2251799813685248}\cdot t^{33}+\frac{6914663035042301}{4503599627370496}\cdot t^{31}-\frac{1879204156221315}{9007199254740992}\cdot t^{29}+\frac{876961939569947}{36028797018963968}\cdot t^{27}-\frac{174201268131891}{72057594037927936}\cdot t^{25}+\frac{1866442158555975}{9223372036854775808}\cdot t^{23}-\frac{260170725132045}{18446744073709551616}\cdot t^{21}+\frac{59516178951775}{73786976294838206464}\cdot t^{19}-\frac{5486397089355}{147573952589676412928}\cdot t^{17}+\frac{797168807855}{590295810358705651712}\cdot t^{15}-\frac{44357564825}{1180591620717411303424}\cdot t^{13}+\frac{3641989533}{4722366482869645213696}\cdot t^{11}-\frac{104819165}{9444732965739290427392}\cdot t^9+\frac{62891499}{604462909807314587353088}\cdot t^7-\frac{685377}{1208925819614629174706176}\cdot t^5+\frac{7095}{4835703278458516698824704}\cdot t^3-\frac{11}{9671406556917033397649408}\cdot t$
• $P_3$:
  $2\cdot t^{175}-87\cdot t^{173}+\frac{7439}{4}\cdot t^{171}-\frac{208335}{8}\cdot t^{169}+\frac{17194905}{64}\cdot t^{167}-\frac{278758571}{128}\cdot t^{165}+\frac{7395300913}{512}\cdot t^{163}-\frac{82536059133}{1024}\cdot t^{161}+\frac{3163882266765}{8192}\cdot t^{159}-\frac{26441467167555}{16384}\cdot t^{157}+\frac{390123140884191}{65536}\cdot t^{155}-\frac{2565355199147559}{131072}\cdot t^{153}+\frac{60629980194487431}{1048576}\cdot t^{151}-\frac{324037057905884925}{2097152}\cdot t^{149}+\frac{3150646032160747075}{8388608}\cdot t^{147}-\frac{13999827151601232655}{16777216}\cdot t^{145}+\frac{3653954886567921722955}{2147483648}\cdot t^{143}-\frac{13724973719320795136205}{4294967296}\cdot t^{141}+\frac{95264058094019864974925}{17179869184}\cdot t^{139}-\frac{306294864626129575921725}{34359738368}\cdot t^{137}+\frac{3658260203662850165752295}{274877906944}\cdot t^{135}-\frac{10165580197275108985938405}{549755813888}\cdot t^{133}+\frac{52676188294971019290771735}{2199023255552}\cdot t^{131}-\frac{127461705976606487428508475}{4398046511104}\cdot t^{129}+\frac{288465966157583103127677075}{8796093022208}\cdot t^{127}-\frac{611395018603131763741601133}{17592186044416}\cdot t^{125}+\frac{2429903279063728804614055785}{70368744177664}\cdot t^{123}-\frac{4531833035748236942833522385}{140737488355328}\cdot t^{121}+\frac{31757826099934556182404799725}{1125899906842624}\cdot t^{119}-\frac{52303940194145090067244686575}{2251799813685248}\cdot t^{117}+\frac{162070565368707114701517097305}{9007199254740992}\cdot t^{115}-\frac{236345396216212488736027713645}{18014398509481984}\cdot t^{113}+\frac{20772134267447119843355324610355}{2305843009213693952}\cdot t^{111}-\frac{26873040835508511685459685684725}{4611686018427387904}\cdot t^{109}+\frac{65523909841674854921547518616525}{18446744073709551616}\cdot t^{107}-\frac{75296067418872969049664838515565}{36893488147419103232}\cdot t^{105}+\frac{326282958815116199215214300234115}{295147905179352825856}\cdot t^{103}-\frac{333261594916547811486976612702665}{590295810358705651712}\cdot t^{101}+\frac{641865390666882703283459913862875}{2361183241434822606848}\cdot t^{99}-\frac{582760436108000747450507962221375}{4722366482869645213696}\cdot t^{97}+\frac{1995097493028567264801150788310825}{37778931862957161709568}\cdot t^{95}-\frac{1609414689498202861307522722639175}{75557863725914323419136}\cdot t^{93}+\frac{2446722118576159147360903414161475}{302231454903657293676544}\cdot t^{91}-\frac{1751936890290150674670903913444875}{604462909807314587353088}\cdot t^{89}+\frac{4724920704115860910476074190805875}{4835703278458516698824704}\cdot t^{87}-\frac{2998461128769709188480236394877825}{9671406556917033397649408}\cdot t^{85}+\frac{3580102417962495586245633421308975}{38685626227668133590597632}\cdot t^{83}-\frac{2009415887898131697178606388374475}{77371252455336267181195264}\cdot t^{81}+\frac{271271144866247779119111862430554125}{39614081257132168796771975168}\cdot t^{79}-\frac{134306025603874241919650272882618875}{79228162514264337593543950336}\cdot t^{77}+\frac{124755374894265406938697364588743755}{316912650057057350374175801344}\cdot t^{75}-\frac{54305280836327294785080029291570811}{633825300114114700748351602688}\cdot t^{73}+\frac{88532430544583207627289278522486409}{5070602400912917605986812821504}\cdot t^{71}-\frac{33747981270638022849181447634357835}{10141204801825835211973625643008}\cdot t^{69}+\frac{24035447498760413358888790573832265}{40564819207303340847894502572032}\cdot t^{67}-\frac{7985330491323707578738259347669893}{81129638414606681695789005144064}\cdot t^{65}+\frac{4943299827962295167790351024748029}{324518553658426726783156020576256}\cdot t^{63}-\frac{1423303046441156193821989613936739}{649037107316853453566312041152512}\cdot t^{61}+\frac{761146865864206848244956456313335}{2596148429267413814265248164610048}\cdot t^{59}-\frac{188660334274034176060715702846895}{5192296858534827628530496329220096}\cdot t^{57}+\frac{173047065230665830455690955025083}{41538374868278621028243970633760768}\cdot t^{55}-\frac{36632201264082502954625954128617}{83076749736557242056487941267521536}\cdot t^{53}+\frac{14283863424421530580496481264639}{332306998946228968225951765070086144}\cdot t^{51}-\frac{2558214056206974503460178903275}{664613997892457936451903530140172288}\cdot t^{49}+\frac{53722495180346464572663756968775}{170141183460469231731687303715884105728}\cdot t^{47}-\frac{8049066845454543063485727135585}{340282366920938463463374607431768211456}\cdot t^{45}+\frac{2195200048760329926405198309705}{1361129467683753853853498429727072845824}\cdot t^{43}-\frac{271431691637762279000944005705}{2722258935367507707706996859454145691648}\cdot t^{41}+\frac{121227661842573566874059958975}{21778071482940061661655974875633165533184}\cdot t^{39}-\frac{12167099746085197487969447325}{43556142965880123323311949751266331066368}\cdot t^{37}+\frac{2184174779216372379241954695}{174224571863520493293247799005065324265472}\cdot t^{35}-\frac{174323808669851316653113755}{348449143727040986586495598010130648530944}\cdot t^{33}+\frac{49168253727393961107288495}{2787593149816327892691964784081045188247552}\cdot t^{31}-\frac{3040728552099772830813825}{5575186299632655785383929568162090376495104}\cdot t^{29}+\frac{327116002160176939403925}{22300745198530623141535718272648361505980416}\cdot t^{27}-\frac{15157454357521070063469}{44601490397061246283071436545296723011960832}\cdot t^{25}+\frac{2393282266977011062653}{356811923176489970264571492362373784095686656}\cdot t^{23}-\frac{79430724589424609583}{713623846352979940529142984724747568191373312}\cdot t^{21}+\frac{4364325526891462065}{2854495385411919762116571938898990272765493248}\cdot t^{19}-\frac{97390012410079605}{5708990770823839524233143877797980545530986496}\cdot t^{17}+\frac{110375347398090219}{730750818665451459101842416358141509827966271488}\cdot t^{15}-\frac{1506096358258541}{1461501637330902918203684832716283019655932542976}\cdot t^{13}+\frac{30481451983437}{5846006549323611672814739330865132078623730171904}\cdot t^{11}-\frac{217188736765}{11692013098647223345629478661730264157247460343808}\cdot t^9+\frac{4046995095}{93536104789177786765035829293842113257979682750464}\cdot t^7-\frac{10987317}{187072209578355573530071658587684226515959365500928}\cdot t^5+\frac{28391}{748288838313422294120286634350736906063837462003712}\cdot t^3-\frac{11}{1496577676626844588240573268701473812127674924007424}\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.