Rule: Q[6, 35, 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.

• $P_1$:
  $64\cdot t^6-80\cdot t^4+24\cdot t^2-1$
• $P_2$:
  $64\cdot t^{41}-640\cdot t^{39}+2964\cdot t^{37}-8436\cdot t^{35}+\frac{66045}{4}\cdot t^{33}-23562\cdot t^{31}+\frac{202895}{8}\cdot t^{29}-\frac{168113}{8}\cdot t^{27}+\frac{3471039}{256}\cdot t^{25}-\frac{876525}{128}\cdot t^{23}+\frac{44352165}{16384}\cdot t^{21}-\frac{13656825}{16384}\cdot t^{19}+\frac{51895935}{262144}\cdot t^{17}-\frac{2340135}{65536}\cdot t^{15}+\frac{5014575}{1048576}\cdot t^{13}-\frac{482885}{1048576}\cdot t^{11}+\frac{2042975}{67108864}\cdot t^9-\frac{43263}{33554432}\cdot t^7+\frac{33649}{1073741824}\cdot t^5-\frac{385}{1073741824}\cdot t^3+\frac{21}{17179869184}\cdot t$
• $P_3$:
  $64\cdot t^{125}-1984\cdot t^{123}+30012\cdot t^{121}-295240\cdot t^{119}+\frac{4247705}{2}\cdot t^{117}-\frac{23822253}{2}\cdot t^{115}+\frac{3470108187}{64}\cdot t^{113}-\frac{3295144749}{16}\cdot t^{111}+\frac{340963706655}{512}\cdot t^{109}-\frac{952949846805}{512}\cdot t^{107}+\frac{37270197111939}{8192}\cdot t^{105}-\frac{40216457753199}{4096}\cdot t^{103}+\frac{1235421360102657}{65536}\cdot t^{101}-\frac{2123511868113825}{65536}\cdot t^{99}+\frac{210227674943268675}{4194304}\cdot t^{97}-\frac{36742494539634345}{524288}\cdot t^{95}+\frac{2982822511263042735}{33554432}\cdot t^{93}-\frac{3443204183265865305}{33554432}\cdot t^{91}+\frac{58024366792072915325}{536870912}\cdot t^{89}-\frac{27941886418809337975}{268435456}\cdot t^{87}+\frac{394455083368927295715}{4294967296}\cdot t^{85}-\frac{319320781774845906055}{4294967296}\cdot t^{83}+\frac{7598941401257346981155}{137438953472}\cdot t^{81}-\frac{1299101421489753282975}{34359738368}\cdot t^{79}+\frac{26160336468038757286575}{1099511627776}\cdot t^{77}-\frac{15157454357521070063469}{1099511627776}\cdot t^{75}+\frac{129421341052679905926543}{17592186044416}\cdot t^{73}-\frac{31810632649311896069487}{8796093022208}\cdot t^{71}+\frac{230464787561341287850365}{140737488355328}\cdot t^{69}-\frac{96102095915198482278165}{140737488355328}\cdot t^{67}+\frac{4721816312633418762600507}{18014398509481984}\cdot t^{65}-\frac{104216658852690057578619}{1125899906842624}\cdot t^{63}+\frac{4330534781687312392575381}{144115188075855872}\cdot t^{61}-\frac{1291117408029941622419835}{144115188075855872}\cdot t^{59}+\frac{5649876944090102598364035}{2305843009213693952}\cdot t^{57}-\frac{707786782006891973860989}{1152921504606846976}\cdot t^{55}+\frac{2595218200691937237490293}{18446744073709551616}\cdot t^{53}-\frac{543001925380122914251689}{18446744073709551616}\cdot t^{51}+\frac{3312571554352424476894275}{590295810358705651712}\cdot t^{49}-\frac{143515478482112112615225}{147573952589676412928}\cdot t^{47}+\frac{721582475530991598777015}{4722366482869645213696}\cdot t^{45}-\frac{102491628518749165393005}{4722366482869645213696}\cdot t^{43}+\frac{209863810776486386280915}{75557863725914323419136}\cdot t^{41}-\frac{12054379716777727427175}{37778931862957161709568}\cdot t^{39}+\frac{19805532971468505595425}{604462909807314587353088}\cdot t^{37}-\frac{1809394370232925202545}{604462909807314587353088}\cdot t^{35}+\frac{9361649132944265178385}{38685626227668133590597632}\cdot t^{33}-\frac{83203453107234244785}{4835703278458516698824704}\cdot t^{31}+\frac{330680390554392511325}{309485009821345068724781056}\cdot t^{29}-\frac{17791709324818892075}{309485009821345068724781056}\cdot t^{27}+\frac{13147136785287223407}{4951760157141521099596496896}\cdot t^{25}-\frac{257786995789945557}{2475880078570760549798248448}\cdot t^{23}+\frac{135592744147310241}{39614081257132168796771975168}\cdot t^{21}-\frac{3679823762074845}{39614081257132168796771975168}\cdot t^{19}+\frac{2589505610348965}{1267650600228229401496703205376}\cdot t^{17}-\frac{11273135819701}{316912650057057350374175801344}\cdot t^{15}+\frac{4831343922729}{10141204801825835211973625643008}\cdot t^{13}-\frac{47908063307}{10141204801825835211973625643008}\cdot t^{11}+\frac{5344712945}{162259276829213363391578010288128}\cdot t^9-\frac{12168585}{81129638414606681695789005144064}\cdot t^7+\frac{516243}{1298074214633706907132624082305024}\cdot t^5-\frac{651}{1298074214633706907132624082305024}\cdot t^3+\frac{63}{332306998946228968225951765070086144}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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