Rule: Q[1, 64, 66]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{65}-\frac{65}{4}\cdot t^{63}+\frac{2015}{16}\cdot t^{61}-\frac{19825}{32}\cdot t^{59}+\frac{556075}{256}\cdot t^{57}-\frac{2958319}{512}\cdot t^{55}+\frac{24819795}{2048}\cdot t^{53}-\frac{84240585}{4096}\cdot t^{51}+\frac{1884328875}{65536}\cdot t^{49}-\frac{4396767375}{131072}\cdot t^{47}+\frac{17283292845}{524288}\cdot t^{45}-\frac{28805488075}{1048576}\cdot t^{43}+\frac{163593432275}{8388608}\cdot t^{41}-\frac{198441737375}{16777216}\cdot t^{39}+\frac{411891673375}{67108864}\cdot t^{37}-\frac{365759805957}{134217728}\cdot t^{35}+\frac{4441369072335}{4294967296}\cdot t^{33}-\frac{2873827046805}{8589934592}\cdot t^{31}+\frac{3159171576275}{34359738368}\cdot t^{29}-\frac{1467532791725}{68719476736}\cdot t^{27}+\frac{2289351155091}{549755813888}\cdot t^{25}-\frac{743295829575}{1099511627776}\cdot t^{23}+\frac{397576839075}{4398046511104}\cdot t^{21}-\frac{86429747625}{8796093022208}\cdot t^{19}+\frac{120158429625}{140737488355328}\cdot t^{17}-\frac{16341546429}{281474976710656}\cdot t^{15}+\frac{3384343935}{1125899906842624}\cdot t^{13}-\frac{257289305}{2251799813685248}\cdot t^{11}+\frac{54636725}{18014398509481984}\cdot t^9-\frac{1884025}{36028797018963968}\cdot t^7+\frac{75361}{144115188075855872}\cdot t^5-\frac{715}{288230376151711744}\cdot t^3+\frac{65}{18446744073709551616}\cdot t$
• $P_3$:
  $t^{131}-33\cdot t^{129}+\frac{8513}{16}\cdot t^{127}-5586\cdot t^{125}+\frac{10993375}{256}\cdot t^{123}-\frac{65978881}{256}\cdot t^{121}+\frac{2575002089}{2048}\cdot t^{119}-\frac{5248828387}{1024}\cdot t^{117}+\frac{1167684031371}{65536}\cdot t^{115}-\frac{3513897647455}{65536}\cdot t^{113}+\frac{74111100549759}{524288}\cdot t^{111}-\frac{43200446040973}{131072}\cdot t^{109}+\frac{5745715806326067}{8388608}\cdot t^{107}-\frac{10710099370076289}{8388608}\cdot t^{105}+\frac{144015429840269745}{67108864}\cdot t^{103}-\frac{109626675635483025}{33554432}\cdot t^{101}+\frac{19422792309354590955}{4294967296}\cdot t^{99}-\frac{24520791120931922355}{4294967296}\cdot t^{97}+\frac{226498747369041217455}{34359738368}\cdot t^{95}-\frac{29966746281884129025}{4294967296}\cdot t^{93}+\frac{3728949859082975799405}{549755813888}\cdot t^{91}-\frac{3335135897584064725515}{549755813888}\cdot t^{89}+\frac{21984603657990826574995}{4398046511104}\cdot t^{87}-\frac{8353790989194114509045}{2199023255552}\cdot t^{85}+\frac{375088326212480555695475}{140737488355328}\cdot t^{83}-\frac{243100047088919822118863}{140737488355328}\cdot t^{81}+\frac{1165016833439724214128207}{1125899906842624}\cdot t^{79}-\frac{161317603033851304334343}{281474976710656}\cdot t^{77}+\frac{5288063829206517494706879}{18014398509481984}\cdot t^{75}-\frac{2504719713950560303075725}{18014398509481984}\cdot t^{73}+\frac{8775503640365100944765229}{144115188075855872}\cdot t^{71}-\frac{1776193912233046993325961}{72057594037927936}\cdot t^{69}+\frac{170059582206273088905527631}{18446744073709551616}\cdot t^{67}-\frac{58724994081754630416975807}{18446744073709551616}\cdot t^{65}+\frac{149673513287554573869528405}{147573952589676412928}\cdot t^{63}-\frac{2746972788689354512326273}{9223372036854775808}\cdot t^{61}+\frac{190122644024236484880353619}{2361183241434822606848}\cdot t^{59}-\frac{47262638560098904593110109}{2361183241434822606848}\cdot t^{57}+\frac{86295507846940179687084549}{18889465931478580854784}\cdot t^{55}-\frac{9026043386474803052153295}{9444732965739290427392}\cdot t^{53}+\frac{110545958776273201389255795}{604462909807314587353088}\cdot t^{51}-\frac{19310696989831575684129015}{604462909807314587353088}\cdot t^{49}+\frac{24574350401525534477683095}{4835703278458516698824704}\cdot t^{47}-\frac{887521302656585485603785}{1208925819614629174706176}\cdot t^{45}+\frac{7429533850850453569289475}{77371252455336267181195264}\cdot t^{43}-\frac{876872821771520637251265}{77371252455336267181195264}\cdot t^{41}+\frac{744255509106316873711185}{618970019642690137449562112}\cdot t^{39}-\frac{35338901127033649504905}{309485009821345068724781056}\cdot t^{37}+\frac{382649248459369840544505}{39614081257132168796771975168}\cdot t^{35}-\frac{28678434491064607396225}{39614081257132168796771975168}\cdot t^{33}+\frac{15140424820045249710557}{316912650057057350374175801344}\cdot t^{31}-\frac{109199954182115596657}{39614081257132168796771975168}\cdot t^{29}+\frac{699486284960938512191}{5070602400912917605986812821504}\cdot t^{27}-\frac{30077269672798161657}{5070602400912917605986812821504}\cdot t^{25}+\frac{8793484000075509425}{40564819207303340847894502572032}\cdot t^{23}-\frac{134817485461505151}{20282409603651670423947251286016}\cdot t^{21}+\frac{218597107440841877}{1298074214633706907132624082305024}\cdot t^{19}-\frac{4491190386670857}{1298074214633706907132624082305024}\cdot t^{17}+\frac{584990111790857}{10384593717069655257060992658440192}\cdot t^{15}-\frac{1832677806365}{2596148429267413814265248164610048}\cdot t^{13}+\frac{1089005439041}{166153499473114484112975882535043072}\cdot t^{11}-\frac{7114304483}{166153499473114484112975882535043072}\cdot t^9+\frac{242964579}{1329227995784915872903807060280344576}\cdot t^7-\frac{302159}{664613997892457936451903530140172288}\cdot t^5+\frac{183105}{340282366920938463463374607431768211456}\cdot t^3-\frac{65}{340282366920938463463374607431768211456}\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.