Rule: Q[3, 18, 22, 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.

• $P_1$:
  $4\cdot t^3-3\cdot t$
• $P_2$:
  $4\cdot t^{21}-21\cdot t^{19}+\frac{189}{4}\cdot t^{17}-\frac{119}{2}\cdot t^{15}+\frac{735}{16}\cdot t^{13}-\frac{5733}{256}\cdot t^{11}+\frac{7007}{1024}\cdot t^9-\frac{1287}{1024}\cdot t^7+\frac{2079}{16384}\cdot t^5-\frac{385}{65536}\cdot t^3+\frac{21}{262144}\cdot t$
• $P_3$:
  $4\cdot t^{43}-44\cdot t^{41}+\frac{901}{4}\cdot t^{39}-\frac{1425}{2}\cdot t^{37}+\frac{99789}{64}\cdot t^{35}-\frac{160293}{64}\cdot t^{33}+\frac{391391}{128}\cdot t^{31}-\frac{5797}{2}\cdot t^{29}+\frac{8850655}{4096}\cdot t^{27}-\frac{5224089}{4096}\cdot t^{25}+\frac{156547365}{262144}\cdot t^{23}-\frac{29004495}{131072}\cdot t^{21}+\frac{270405135}{4194304}\cdot t^{19}-\frac{61256475}{4194304}\cdot t^{17}+\frac{42456735}{16777216}\cdot t^{15}-\frac{1374365}{4194304}\cdot t^{13}+\frac{32947615}{1073741824}\cdot t^{11}-\frac{2129501}{1073741824}\cdot t^9+\frac{1418065}{17179869184}\cdot t^7-\frac{17017}{8589934592}\cdot t^5+\frac{6181}{274877906944}\cdot t^3-\frac{21}{274877906944}\cdot t$
• $P_4$:
  $4\cdot t^{127}-128\cdot t^{125}+\frac{7999}{4}\cdot t^{123}-\frac{81313}{4}\cdot t^{121}+\frac{4838185}{32}\cdot t^{119}-\frac{14034979}{16}\cdot t^{117}+\frac{4232420283}{1024}\cdot t^{115}-\frac{16650687183}{1024}\cdot t^{113}+\frac{446408338623}{8192}\cdot t^{111}-\frac{323478388365}{2048}\cdot t^{109}+\frac{52517394660819}{131072}\cdot t^{107}-\frac{117703112618337}{131072}\cdot t^{105}+\frac{1878884684153841}{1048576}\cdot t^{103}-\frac{1679466614108241}{524288}\cdot t^{101}+\frac{346132434502553475}{67108864}\cdot t^{99}-\frac{504167631260343435}{67108864}\cdot t^{97}+\frac{5334342161799640815}{536870912}\cdot t^{95}-\frac{803253336816113505}{67108864}\cdot t^{93}+\frac{113115633724326760205}{8589934592}\cdot t^{91}-\frac{113908139629691591275}{8589934592}\cdot t^{89}+\frac{841525266069876703315}{68719476736}\cdot t^{87}-\frac{356887932571886600885}{34359738368}\cdot t^{85}+\frac{17817206418052415974915}{2199023255552}\cdot t^{83}-\frac{12795347087216360113055}{2199023255552}\cdot t^{81}+\frac{67731581955710862341775}{17592186044416}\cdot t^{79}-\frac{10329447706389956837511}{4398046511104}\cdot t^{77}+\frac{371940610773017026942047}{281474976710656}\cdot t^{75}-\frac{193042606351303698065517}{281474976710656}\cdot t^{73}+\frac{739434909950331624962157}{2251799813685248}\cdot t^{71}-\frac{163283441738269885064265}{1125899906842624}\cdot t^{69}+\frac{17022884589778824494205627}{288230376151711744}\cdot t^{67}-\frac{6389282854276459683858411}{288230376151711744}\cdot t^{65}+\frac{17670267114831639762638613}{2305843009213693952}\cdot t^{63}-\frac{351353261857328375937201}{144115188075855872}\cdot t^{61}+\frac{26307755472569168557081395}{36893488147419103232}\cdot t^{59}-\frac{7065450508103886546086013}{36893488147419103232}\cdot t^{57}+\frac{13919806712802208819266117}{295147905179352825856}\cdot t^{55}-\frac{1569110063036030075870991}{147573952589676412928}\cdot t^{53}+\frac{20688633166516357732948323}{9444732965739290427392}\cdot t^{51}-\frac{3886633468280872927355175}{9444732965739290427392}\cdot t^{49}+\frac{5314077786958579202464215}{75557863725914323419136}\cdot t^{47}-\frac{206018526012435191042505}{18889465931478580854784}\cdot t^{45}+\frac{1849729867076473032568995}{1208925819614629174706176}\cdot t^{43}-\frac{233972570210041841135265}{1208925819614629174706176}\cdot t^{41}+\frac{212675608439912144430225}{9671406556917033397649408}\cdot t^{39}-\frac{10807463670850715398985}{4835703278458516698824704}\cdot t^{37}+\frac{125162888827851478141265}{618970019642690137449562112}\cdot t^{35}-\frac{10027276757802139136665}{618970019642690137449562112}\cdot t^{33}+\frac{5655701389417384177565}{4951760157141521099596496896}\cdot t^{31}-\frac{43559012484901425425}{618970019642690137449562112}\cdot t^{29}+\frac{297814485982389496607}{79228162514264337593543950336}\cdot t^{27}-\frac{13662710776867114521}{79228162514264337593543950336}\cdot t^{25}+\frac{4260184676786439153}{633825300114114700748351602688}\cdot t^{23}-\frac{69636283954692543}{316912650057057350374175801344}\cdot t^{21}+\frac{120343865996744005}{20282409603651670423947251286016}\cdot t^{19}-\frac{2634598153627769}{20282409603651670423947251286016}\cdot t^{17}+\frac{365571690153161}{162259276829213363391578010288128}\cdot t^{15}-\frac{1219812996509}{40564819207303340847894502572032}\cdot t^{13}+\frac{771873725857}{2596148429267413814265248164610048}\cdot t^{11}-\frac{5369050115}{2596148429267413814265248164610048}\cdot t^9+\frac{195213603}{20769187434139310514121985316880384}\cdot t^7-\frac{258447}{10384593717069655257060992658440192}\cdot t^5+\frac{166719}{5316911983139663491615228241121378304}\cdot t^3-\frac{63}{5316911983139663491615228241121378304}\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.