Rule: Q[1, 4, 40, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{45}-\frac{45}{4}\cdot t^{43}+\frac{945}{16}\cdot t^{41}-\frac{3075}{16}\cdot t^{39}+\frac{55575}{128}\cdot t^{37}-\frac{740259}{1024}\cdot t^{35}+\frac{3764565}{4096}\cdot t^{33}-\frac{934065}{1024}\cdot t^{31}+\frac{11738925}{16384}\cdot t^{29}-\frac{29419775}{65536}\cdot t^{27}+\frac{59007663}{262144}\cdot t^{25}-\frac{23666175}{262144}\cdot t^{23}+\frac{60480225}{2097152}\cdot t^{21}-\frac{488494125}{67108864}\cdot t^{19}+\frac{384942375}{268435456}\cdot t^{17}-\frac{29084535}{134217728}\cdot t^{15}+\frac{105306075}{4294967296}\cdot t^{13}-\frac{34512075}{17179869184}\cdot t^{11}+\frac{7811375}{68719476736}\cdot t^9-\frac{284625}{68719476736}\cdot t^7+\frac{47817}{549755813888}\cdot t^5-\frac{3795}{4398046511104}\cdot t^3+\frac{45}{17592186044416}\cdot t$
• $P_4$:
  $t^{135}-\frac{135}{4}\cdot t^{133}+\frac{4455}{8}\cdot t^{131}-\frac{383175}{64}\cdot t^{129}+\frac{377325}{8}\cdot t^{127}-\frac{9289161}{32}\cdot t^{125}+\frac{93011625}{64}\cdot t^{123}-\frac{99695174625}{16384}\cdot t^{121}+\frac{1424777495625}{65536}\cdot t^{119}-\frac{17642615161875}{262144}\cdot t^{117}+\frac{95778229190787}{524288}\cdot t^{115}-\frac{1841132822127885}{4194304}\cdot t^{113}+\frac{3946710195943515}{4194304}\cdot t^{111}-\frac{30384193879237275}{16777216}\cdot t^{109}+\frac{105573415096334475}{33554432}\cdot t^{107}-\frac{2660919275605834701}{536870912}\cdot t^{105}+\frac{30522309337831633335}{4294967296}\cdot t^{103}-\frac{159854128565931774585}{17179869184}\cdot t^{101}+\frac{383315930321916173625}{34359738368}\cdot t^{99}-\frac{3374710667861370886125}{274877906944}\cdot t^{97}+\frac{1707897051039406831065}{137438953472}\cdot t^{95}-\frac{6370727095146993734925}{549755813888}\cdot t^{93}+\frac{10962980898245711664525}{1099511627776}\cdot t^{91}-\frac{278841035890162666249875}{35184372088832}\cdot t^{89}+\frac{819775898307715466242125}{140737488355328}\cdot t^{87}-\frac{2230386644050300770335847}{562949953421312}\cdot t^{85}+\frac{2809626083013258203986935}{1125899906842624}\cdot t^{83}-\frac{13115442469813604483083045}{9007199254740992}\cdot t^{81}+\frac{7091794659912563171760525}{9007199254740992}\cdot t^{79}-\frac{14215887668959406071694325}{36028797018963968}\cdot t^{77}+\frac{13204980101388959417707173}{72057594037927936}\cdot t^{75}-\frac{90927592509564174650465025}{1152921504606846976}\cdot t^{73}+\frac{579994449308579249954907975}{18446744073709551616}\cdot t^{71}-\frac{856379207683790514639302625}{73786976294838206464}\cdot t^{69}+\frac{585051141882985599110018625}{147573952589676412928}\cdot t^{67}-\frac{1478340656803749896722572777}{1180591620717411303424}\cdot t^{65}+\frac{107847522662450890333296555}{295147905179352825856}\cdot t^{63}-\frac{116175516690439376073319455}{1180591620717411303424}\cdot t^{61}+\frac{57678023750272397779211775}{2361183241434822606848}\cdot t^{59}-\frac{843479475527487800001977325}{151115727451828646838272}\cdot t^{57}+\frac{708522759443089752001660953}{604462909807314587353088}\cdot t^{55}-\frac{546007419705754167992976915}{2417851639229258349412352}\cdot t^{53}+\frac{192626273516264527264291395}{4835703278458516698824704}\cdot t^{51}-\frac{248330130165052853652145125}{38685626227668133590597632}\cdot t^{49}+\frac{36468061073189579906958375}{38685626227668133590597632}\cdot t^{47}-\frac{19467641491416264631813335}{154742504910672534362390528}\cdot t^{45}+\frac{4707612378236957006715975}{309485009821345068724781056}\cdot t^{43}-\frac{8222386803767837866662525}{4951760157141521099596496896}\cdot t^{41}+\frac{6458196531695045067685125}{39614081257132168796771975168}\cdot t^{39}-\frac{2271249943040355194662875}{158456325028528675187087900672}\cdot t^{37}+\frac{355918226368206249328347}{316912650057057350374175801344}\cdot t^{35}-\frac{197732347982336805182415}{2535301200456458802993406410752}\cdot t^{33}+\frac{6047421207986204421705}{1267650600228229401496703205376}\cdot t^{31}-\frac{1294086912891663624525}{5070602400912917605986812821504}\cdot t^{29}+\frac{120118721224054739725}{10141204801825835211973625643008}\cdot t^{27}-\frac{153315167816884413249}{324518553658426726783156020576256}\cdot t^{25}+\frac{20793196358528627475}{1298074214633706907132624082305024}\cdot t^{23}-\frac{2366477138420037225}{5192296858534827628530496329220096}\cdot t^{21}+\frac{111276354471161625}{10384593717069655257060992658440192}\cdot t^{19}-\frac{16974359156617875}{83076749736557242056487941267521536}\cdot t^{17}+\frac{256501427255559}{83076749736557242056487941267521536}\cdot t^{15}-\frac{11932941897135}{332306998946228968225951765070086144}\cdot t^{13}+\frac{205649462655}{664613997892457936451903530140172288}\cdot t^{11}-\frac{19948360575}{10633823966279326983230456482242756608}\cdot t^9+\frac{2528665425}{340282366920938463463374607431768211456}\cdot t^7-\frac{23341527}{1361129467683753853853498429727072845824}\cdot t^5+\frac{51255}{2722258935367507707706996859454145691648}\cdot t^3-\frac{135}{21778071482940061661655974875633165533184}\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.