Rule: Q[1, 88, 90]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{89}-\frac{89}{4}\cdot t^{87}+\frac{3827}{16}\cdot t^{85}-\frac{52955}{32}\cdot t^{83}+\frac{2120069}{256}\cdot t^{81}-\frac{8177409}{256}\cdot t^{79}+\frac{101183121}{1024}\cdot t^{77}-\frac{515787129}{2048}\cdot t^{75}+\frac{17670484975}{32768}\cdot t^{73}-\frac{257989080635}{262144}\cdot t^{71}+\frac{1623045228805}{1048576}\cdot t^{69}-\frac{4437836954285}{2097152}\cdot t^{67}+\frac{42476439419585}{16777216}\cdot t^{65}-\frac{11178010373575}{4194304}\cdot t^{63}+\frac{41582198589699}{16777216}\cdot t^{61}-\frac{68554435512747}{33554432}\cdot t^{59}+\frac{1606803276196029}{1073741824}\cdot t^{57}-\frac{4190290896746507}{4294967296}\cdot t^{55}+\frac{9737999971312305}{17179869184}\cdot t^{53}-\frac{10089446586818313}{34359738368}\cdot t^{51}+\frac{37287085212154635}{274877906944}\cdot t^{49}-\frac{15353505675593085}{274877906944}\cdot t^{47}+\frac{22519863819967605}{1099511627776}\cdot t^{45}-\frac{14686867708674525}{2199023255552}\cdot t^{43}+\frac{68011495081708185}{35184372088832}\cdot t^{41}-\frac{557694259670007117}{1125899906842624}\cdot t^{39}+\frac{504580520653815963}{4503599627370496}\cdot t^{37}-\frac{200747088862270867}{9007199254740992}\cdot t^{35}+\frac{279729550053983995}{72057594037927936}\cdot t^{33}-\frac{21220862417888441}{36028797018963968}\cdot t^{31}+\frac{11149944660246469}{144115188075855872}\cdot t^{29}-\frac{2517729439410493}{288230376151711744}\cdot t^{27}+\frac{15503912863738299}{18446744073709551616}\cdot t^{25}-\frac{5033737942772175}{73786976294838206464}\cdot t^{23}+\frac{1362070266867765}{295147905179352825856}\cdot t^{21}-\frac{151341140763085}{590295810358705651712}\cdot t^{19}+\frac{54254371216955}{4722366482869645213696}\cdot t^{17}-\frac{1917514159435}{4722366482869645213696}\cdot t^{15}+\frac{207780172075}{18889465931478580854784}\cdot t^{13}-\frac{8311206883}{37778931862957161709568}\cdot t^{11}+\frac{1865781137}{604462909807314587353088}\cdot t^9-\frac{136520571}{4835703278458516698824704}\cdot t^7+\frac{2904693}{19342813113834066795298816}\cdot t^5-\frac{14685}{38685626227668133590597632}\cdot t^3+\frac{89}{309485009821345068724781056}\cdot t$
• $P_3$:
  $t^{179}-45\cdot t^{177}+\frac{15929}{16}\cdot t^{175}-\frac{57739}{4}\cdot t^{173}+\frac{39493651}{256}\cdot t^{171}-\frac{331794321}{256}\cdot t^{169}+\frac{18255257475}{2048}\cdot t^{167}-\frac{52844660531}{1024}\cdot t^{165}+\frac{16822196633957}{65536}\cdot t^{163}-\frac{73007729639757}{65536}\cdot t^{161}+\frac{1119381545981457}{262144}\cdot t^{159}-\frac{478350178758495}{32768}\cdot t^{157}+\frac{188193038779861713}{4194304}\cdot t^{155}-\frac{523529795641421079}{4194304}\cdot t^{153}+\frac{10604916425886334497}{33554432}\cdot t^{151}-\frac{12279461461023963015}{16777216}\cdot t^{149}+\frac{3342835440122552646575}{2147483648}\cdot t^{147}-\frac{6552742626193588719755}{2147483648}\cdot t^{145}+\frac{380035190261146002466555}{68719476736}\cdot t^{143}-\frac{159643115366836617110595}{17179869184}\cdot t^{141}+\frac{15955225561410000753852965}{1099511627776}\cdot t^{139}-\frac{23205482362865340728164975}{1099511627776}\cdot t^{137}+\frac{251944855324988239337460005}{8796093022208}\cdot t^{135}-\frac{159796491875743511609000145}{4398046511104}\cdot t^{133}+\frac{12143769959537739186352260705}{281474976710656}\cdot t^{131}-\frac{13516039301759351926919038689}{281474976710656}\cdot t^{129}+\frac{14117080589958028477679088855}{281474976710656}\cdot t^{127}-\frac{865707476483636713901925251}{17592186044416}\cdot t^{125}+\frac{204459004481219466559668408195}{4503599627370496}\cdot t^{123}-\frac{177500514616917398682114958045}{4503599627370496}\cdot t^{121}+\frac{1160876305321975581279123495235}{36028797018963968}\cdot t^{119}-\frac{447114327466078995736123933625}{18014398509481984}\cdot t^{117}+\frac{83121287703131432794820010646845}{4611686018427387904}\cdot t^{115}-\frac{56930592561293123423111645326185}{4611686018427387904}\cdot t^{113}+\frac{588617858198942716844598209145835}{73786976294838206464}\cdot t^{111}-\frac{89742406958244391124383857908485}{18446744073709551616}\cdot t^{109}+\frac{3306357291852132758660310502887825}{1180591620717411303424}\cdot t^{107}-\frac{1796930473807157612725785200249835}{1180591620717411303424}\cdot t^{105}+\frac{7376408342032207331617924429048065}{9444732965739290427392}\cdot t^{103}-\frac{1786839833472934487230442756096745}{4722366482869645213696}\cdot t^{101}+\frac{52307091913268887373730571749717675}{302231454903657293676544}\cdot t^{99}-\frac{22585520316478370431679442730969875}{302231454903657293676544}\cdot t^{97}+\frac{36817774758107903914547601481382925}{1208925819614629174706176}\cdot t^{95}-\frac{1769821469182409126554119671739425}{151115727451828646838272}\cdot t^{93}+\frac{82179861094755687894551104737385525}{19342813113834066795298816}\cdot t^{91}-\frac{28112393372878114765476747039379075}{19342813113834066795298816}\cdot t^{89}+\frac{72517261241430387017306703884977125}{154742504910672534362390528}\cdot t^{87}-\frac{11014698559060606093852931289602075}{77371252455336267181195264}\cdot t^{85}+\frac{403282033365236293591059543479790425}{9903520314283042199192993792}\cdot t^{83}-\frac{108549466434007236784321859388310925}{9903520314283042199192993792}\cdot t^{81}+\frac{3516781266629290596073971826334391885}{1267650600228229401496703205376}\cdot t^{79}-\frac{209096047704855192321965326801567425}{316912650057057350374175801344}\cdot t^{77}+\frac{2987919453915596375233145478589233915}{20282409603651670423947251286016}\cdot t^{75}-\frac{625732401392746579533745069006938561}{20282409603651670423947251286016}\cdot t^{73}+\frac{982270719606112919286143867995469403}{162259276829213363391578010288128}\cdot t^{71}-\frac{90199149941523442887812232768192759}{81129638414606681695789005144064}\cdot t^{69}+\frac{991072023487848213174959871063862875}{5192296858534827628530496329220096}\cdot t^{67}-\frac{158846035362496909905878607625202859}{5192296858534827628530496329220096}\cdot t^{65}+\frac{47468238456893836175642009567952489}{10384593717069655257060992658440192}\cdot t^{63}-\frac{25787489444579685568954808902419}{40564819207303340847894502572032}\cdot t^{61}+\frac{13649900461164776145192885783219141}{166153499473114484112975882535043072}\cdot t^{59}-\frac{1636087161163345559608501750918155}{166153499473114484112975882535043072}\cdot t^{57}+\frac{1452186080457660530672321398885797}{1329227995784915872903807060280344576}\cdot t^{55}-\frac{74408572664933583830517747070263}{664613997892457936451903530140172288}\cdot t^{53}+\frac{3597493031036451201916470924222651}{340282366920938463463374607431768211456}\cdot t^{51}-\frac{312220186275229672860763065225855}{340282366920938463463374607431768211456}\cdot t^{49}+\frac{397346100716175599275203032312175}{5444517870735015415413993718908291383296}\cdot t^{47}-\frac{7219040956371035230616099914005}{1361129467683753853853498429727072845824}\cdot t^{45}+\frac{30572834392875428992594961182485}{87112285931760246646623899502532662132736}\cdot t^{43}-\frac{1835229962812525690329485856135}{87112285931760246646623899502532662132736}\cdot t^{41}+\frac{796187140573523537966652177765}{696898287454081973172991196020261297061888}\cdot t^{39}-\frac{19413501204518232611589077925}{348449143727040986586495598010130648530944}\cdot t^{37}+\frac{54207868268532784917681000795}{22300745198530623141535718272648361505980416}\cdot t^{35}-\frac{2103825690933411095498537235}{22300745198530623141535718272648361505980416}\cdot t^{33}+\frac{288656423308139963449934715}{89202980794122492566142873090593446023921664}\cdot t^{31}-\frac{1085896214461576531652793}{11150372599265311570767859136324180752990208}\cdot t^{29}+\frac{3639595939824284473157355}{1427247692705959881058285969449495136382746624}\cdot t^{27}-\frac{82127915715700288717101}{1427247692705959881058285969449495136382746624}\cdot t^{25}+\frac{12634266992469715743003}{11417981541647679048466287755595961091061972992}\cdot t^{23}-\frac{102169413030798353709}{5708990770823839524233143877797980545530986496}\cdot t^{21}+\frac{175136516270269785297}{730750818665451459101842416358141509827966271488}\cdot t^{19}-\frac{1905718144073779925}{730750818665451459101842416358141509827966271488}\cdot t^{17}+\frac{526750641647796411}{23384026197294446691258957323460528314494920687616}\cdot t^{15}-\frac{876749011375307}{5846006549323611672814739330865132078623730171904}\cdot t^{13}+\frac{277131135732373}{374144419156711147060143317175368453031918731001856}\cdot t^{11}-\frac{964025972767}{374144419156711147060143317175368453031918731001856}\cdot t^9+\frac{17544360405}{2993155353253689176481146537402947624255349848014848}\cdot t^7-\frac{11633457}{1496577676626844588240573268701473812127674924007424}\cdot t^5+\frac{470009}{95780971304118053647396689196894323976171195136475136}\cdot t^3-\frac{89}{95780971304118053647396689196894323976171195136475136}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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