Rule: Q[2, 40, 84]

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.

• $P_1$:
  $2\cdot t^2-1$
• $P_2$:
  $2\cdot t^{42}-21\cdot t^{40}+\frac{819}{8}\cdot t^{38}-\frac{4921}{16}\cdot t^{36}+\frac{81585}{128}\cdot t^{34}-\frac{247401}{256}\cdot t^{32}+\frac{284053}{256}\cdot t^{30}-\frac{504339}{512}\cdot t^{28}+\frac{5607063}{8192}\cdot t^{26}-\frac{6135675}{16384}\cdot t^{24}+\frac{84672315}{524288}\cdot t^{22}-\frac{57358665}{1048576}\cdot t^{20}+\frac{121090515}{8388608}\cdot t^{18}-\frac{49142835}{16777216}\cdot t^{16}+\frac{15043725}{33554432}\cdot t^{14}-\frac{3380195}{67108864}\cdot t^{12}+\frac{8580495}{2147483648}\cdot t^{10}-\frac{908523}{4294967296}\cdot t^8+\frac{235543}{34359738368}\cdot t^6-\frac{8085}{68719476736}\cdot t^4+\frac{441}{549755813888}\cdot t^2-\frac{1}{1099511627776}$
• $P_3$:
  $2\cdot t^{126}-63\cdot t^{124}+\frac{7749}{8}\cdot t^{122}-\frac{155001}{16}\cdot t^{120}+\frac{4535685}{64}\cdot t^{118}-\frac{51751791}{128}\cdot t^{116}+\frac{3835382733}{2048}\cdot t^{114}-\frac{29656302741}{4096}\cdot t^{112}+\frac{390558427623}{16384}\cdot t^{110}-\frac{2223549642545}{32768}\cdot t^{108}+\frac{44302309774569}{262144}\cdot t^{106}-\frac{194895141419349}{524288}\cdot t^{104}+\frac{1526108738950341}{2097152}\cdot t^{102}-\frac{5351249907646839}{4194304}\cdot t^{100}+\frac{270292724927059725}{134217728}\cdot t^{98}-\frac{771592385332321245}{268435456}\cdot t^{96}+\frac{3998251451267482815}{1073741824}\cdot t^{94}-\frac{9431385371554326705}{2147483648}\cdot t^{92}+\frac{81234113508902081455}{17179869184}\cdot t^{90}-\frac{160030804034998935675}{34359738368}\cdot t^{88}+\frac{577922564005637665815}{137438953472}\cdot t^{86}-\frac{957962345324537718165}{274877906944}\cdot t^{84}+\frac{11676422153151533166165}{4398046511104}\cdot t^{82}-\frac{16368677910770891365485}{8796093022208}\cdot t^{80}+\frac{42259005063754915616775}{35184372088832}\cdot t^{78}-\frac{50258927606517232315713}{70368744177664}\cdot t^{76}+\frac{220366067197806326307357}{562949953421312}\cdot t^{74}-\frac{222674428545183272486409}{1125899906842624}\cdot t^{72}+\frac{414836617610414318130657}{4503599627370496}\cdot t^{70}-\frac{356143061332794375501435}{9007199254740992}\cdot t^{68}+\frac{9014376596845617637691877}{576460752303423488}\cdot t^{66}-\frac{6565649507719473627452997}{1152921504606846976}\cdot t^{64}+\frac{8800764233751634862330613}{4611686018427387904}\cdot t^{62}-\frac{5422693113725754814163307}{9223372036854775808}\cdot t^{60}+\frac{12273870602678498748170145}{73786976294838206464}\cdot t^{58}-\frac{6370081038062027764748901}{147573952589676412928}\cdot t^{56}+\frac{6055509134947853554144017}{590295810358705651712}\cdot t^{54}-\frac{2631470869149826430604339}{1180591620717411303424}\cdot t^{52}+\frac{8347680316968109681773573}{18889465931478580854784}\cdot t^{50}-\frac{3013825048124354364919725}{37778931862957161709568}\cdot t^{48}+\frac{1976508519932716118389215}{151115727451828646838272}\cdot t^{46}-\frac{586997508789199765432665}{302231454903657293676544}\cdot t^{44}+\frac{629591432329459158842745}{2417851639229258349412352}\cdot t^{42}-\frac{151885184431399365582405}{4835703278458516698824704}\cdot t^{40}+\frac{65670977747500834342725}{19342813113834066795298816}\cdot t^{38}-\frac{12665760591630476417815}{38685626227668133590597632}\cdot t^{36}+\frac{34693170316205218014015}{1237940039285380274899124224}\cdot t^{34}-\frac{5241817545755757421455}{2475880078570760549798248448}\cdot t^{32}+\frac{1388857640328448547565}{9903520314283042199192993792}\cdot t^{30}-\frac{160125383923370028675}{19807040628566084398385987584}\cdot t^{28}+\frac{63713047497930390357}{158456325028528675187087900672}\cdot t^{26}-\frac{5413526911588856697}{316912650057057350374175801344}\cdot t^{24}+\frac{776576625570958653}{1267650600228229401496703205376}\cdot t^{22}-\frac{46365779402143047}{2535301200456458802993406410752}\cdot t^{20}+\frac{18126539272442755}{40564819207303340847894502572032}\cdot t^{18}-\frac{710207556641163}{81129638414606681695789005144064}\cdot t^{16}+\frac{43482095304561}{324518553658426726783156020576256}\cdot t^{14}-\frac{1006069329447}{649037107316853453566312041152512}\cdot t^{12}+\frac{67343383107}{5192296858534827628530496329220096}\cdot t^{10}-\frac{766620855}{10384593717069655257060992658440192}\cdot t^8+\frac{10841103}{41538374868278621028243970633760768}\cdot t^6-\frac{41013}{83076749736557242056487941267521536}\cdot t^4+\frac{3969}{10633823966279326983230456482242756608}\cdot t^2-\frac{1}{21267647932558653966460912964485513216}$

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.