Rule: Q[14, 28, 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.

• $P_1$:
  $8192\cdot t^{14}-28672\cdot t^{12}+39424\cdot t^{10}-26880\cdot t^8+9408\cdot t^6-1568\cdot t^4+98\cdot t^2-1$
• $P_2$:
  $8192\cdot t^{42}-86016\cdot t^{40}+419328\cdot t^{38}-1259776\cdot t^{36}+2610720\cdot t^{34}-3958416\cdot t^{32}+4544848\cdot t^{30}-4034712\cdot t^{28}+\frac{5607063}{2}\cdot t^{26}-\frac{6135675}{4}\cdot t^{24}+\frac{84672315}{128}\cdot t^{22}-\frac{57358665}{256}\cdot t^{20}+\frac{121090515}{2048}\cdot t^{18}-\frac{49142835}{4096}\cdot t^{16}+\frac{15043725}{8192}\cdot t^{14}-\frac{3380195}{16384}\cdot t^{12}+\frac{8580495}{524288}\cdot t^{10}-\frac{908523}{1048576}\cdot t^8+\frac{235543}{8388608}\cdot t^6-\frac{8085}{16777216}\cdot t^4+\frac{441}{134217728}\cdot t^2-\frac{1}{268435456}$
• $P_3$:
  $8192\cdot t^{126}-258048\cdot t^{124}+3967488\cdot t^{122}-39680256\cdot t^{120}+290283840\cdot t^{118}-1656057312\cdot t^{116}+7670765466\cdot t^{114}-29656302741\cdot t^{112}+\frac{390558427623}{4}\cdot t^{110}-\frac{2223549642545}{8}\cdot t^{108}+\frac{44302309774569}{64}\cdot t^{106}-\frac{194895141419349}{128}\cdot t^{104}+\frac{1526108738950341}{512}\cdot t^{102}-\frac{5351249907646839}{1024}\cdot t^{100}+\frac{270292724927059725}{32768}\cdot t^{98}-\frac{771592385332321245}{65536}\cdot t^{96}+\frac{3998251451267482815}{262144}\cdot t^{94}-\frac{9431385371554326705}{524288}\cdot t^{92}+\frac{81234113508902081455}{4194304}\cdot t^{90}-\frac{160030804034998935675}{8388608}\cdot t^{88}+\frac{577922564005637665815}{33554432}\cdot t^{86}-\frac{957962345324537718165}{67108864}\cdot t^{84}+\frac{11676422153151533166165}{1073741824}\cdot t^{82}-\frac{16368677910770891365485}{2147483648}\cdot t^{80}+\frac{42259005063754915616775}{8589934592}\cdot t^{78}-\frac{50258927606517232315713}{17179869184}\cdot t^{76}+\frac{220366067197806326307357}{137438953472}\cdot t^{74}-\frac{222674428545183272486409}{274877906944}\cdot t^{72}+\frac{414836617610414318130657}{1099511627776}\cdot t^{70}-\frac{356143061332794375501435}{2199023255552}\cdot t^{68}+\frac{9014376596845617637691877}{140737488355328}\cdot t^{66}-\frac{6565649507719473627452997}{281474976710656}\cdot t^{64}+\frac{8800764233751634862330613}{1125899906842624}\cdot t^{62}-\frac{5422693113725754814163307}{2251799813685248}\cdot t^{60}+\frac{12273870602678498748170145}{18014398509481984}\cdot t^{58}-\frac{6370081038062027764748901}{36028797018963968}\cdot t^{56}+\frac{6055509134947853554144017}{144115188075855872}\cdot t^{54}-\frac{2631470869149826430604339}{288230376151711744}\cdot t^{52}+\frac{8347680316968109681773573}{4611686018427387904}\cdot t^{50}-\frac{3013825048124354364919725}{9223372036854775808}\cdot t^{48}+\frac{1976508519932716118389215}{36893488147419103232}\cdot t^{46}-\frac{586997508789199765432665}{73786976294838206464}\cdot t^{44}+\frac{629591432329459158842745}{590295810358705651712}\cdot t^{42}-\frac{151885184431399365582405}{1180591620717411303424}\cdot t^{40}+\frac{65670977747500834342725}{4722366482869645213696}\cdot t^{38}-\frac{12665760591630476417815}{9444732965739290427392}\cdot t^{36}+\frac{34693170316205218014015}{302231454903657293676544}\cdot t^{34}-\frac{5241817545755757421455}{604462909807314587353088}\cdot t^{32}+\frac{1388857640328448547565}{2417851639229258349412352}\cdot t^{30}-\frac{160125383923370028675}{4835703278458516698824704}\cdot t^{28}+\frac{63713047497930390357}{38685626227668133590597632}\cdot t^{26}-\frac{5413526911588856697}{77371252455336267181195264}\cdot t^{24}+\frac{776576625570958653}{309485009821345068724781056}\cdot t^{22}-\frac{46365779402143047}{618970019642690137449562112}\cdot t^{20}+\frac{18126539272442755}{9903520314283042199192993792}\cdot t^{18}-\frac{710207556641163}{19807040628566084398385987584}\cdot t^{16}+\frac{43482095304561}{79228162514264337593543950336}\cdot t^{14}-\frac{1006069329447}{158456325028528675187087900672}\cdot t^{12}+\frac{67343383107}{1267650600228229401496703205376}\cdot t^{10}-\frac{766620855}{2535301200456458802993406410752}\cdot t^8+\frac{10841103}{10141204801825835211973625643008}\cdot t^6-\frac{41013}{20282409603651670423947251286016}\cdot t^4+\frac{3969}{2596148429267413814265248164610048}\cdot t^2-\frac{1}{5192296858534827628530496329220096}$

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.