Rule: Q[1, 60, 62]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{61}-\frac{61}{4}\cdot t^{59}+\frac{1769}{16}\cdot t^{57}-\frac{8113}{16}\cdot t^{55}+\frac{211365}{128}\cdot t^{53}-\frac{4160871}{1024}\cdot t^{51}+\frac{32152185}{4096}\cdot t^{49}-\frac{25007255}{2048}\cdot t^{47}+\frac{510053635}{32768}\cdot t^{45}-\frac{2157919225}{131072}\cdot t^{43}+\frac{7641572785}{524288}\cdot t^{41}-\frac{5696445167}{524288}\cdot t^{39}+\frac{28714733801}{4194304}\cdot t^{37}-\frac{245179650147}{67108864}\cdot t^{35}+\frac{443410005585}{268435456}\cdot t^{33}-\frac{42413130969}{67108864}\cdot t^{31}+\frac{438269020013}{2147483648}\cdot t^{29}-\frac{475767973597}{8589934592}\cdot t^{27}+\frac{431510487681}{34359738368}\cdot t^{25}-\frac{81110993925}{34359738368}\cdot t^{23}+\frac{100102836405}{274877906944}\cdot t^{21}-\frac{100102836405}{2199023255552}\cdot t^{19}+\frac{39901130595}{8796093022208}\cdot t^{17}-\frac{1552217895}{4398046511104}\cdot t^{15}+\frac{1468314225}{70368744177664}\cdot t^{13}-\frac{254507799}{281474976710656}\cdot t^{11}+\frac{30764679}{1125899906842624}\cdot t^9-\frac{603229}{1125899906842624}\cdot t^7+\frac{54839}{9007199254740992}\cdot t^5-\frac{9455}{288230376151711744}\cdot t^3+\frac{61}{1152921504606846976}\cdot t$
• $P_3$:
  $t^{123}-31\cdot t^{121}+\frac{7501}{16}\cdot t^{119}-\frac{36875}{8}\cdot t^{117}+\frac{8481369}{256}\cdot t^{115}-\frac{47511077}{256}\cdot t^{113}+\frac{863821833}{1024}\cdot t^{111}-\frac{818777773}{256}\cdot t^{109}+\frac{338153196645}{32768}\cdot t^{107}-\frac{942679901031}{32768}\cdot t^{105}+\frac{73519220560071}{1048576}\cdot t^{103}-\frac{79063252382283}{524288}\cdot t^{101}+\frac{4838983415292585}{16777216}\cdot t^{99}-\frac{8281854245862225}{16777216}\cdot t^{97}+\frac{25499447836838255}{33554432}\cdot t^{95}-\frac{1108253812524495}{1048576}\cdot t^{93}+\frac{2862174580496588035}{2147483648}\cdot t^{91}-\frac{3282644102618267205}{2147483648}\cdot t^{89}+\frac{54927850951012094825}{34359738368}\cdot t^{87}-\frac{26246504533705429435}{17179869184}\cdot t^{85}+\frac{734803930507762746785}{549755813888}\cdot t^{83}-\frac{589392648054277490885}{549755813888}\cdot t^{81}+\frac{1735797226835887549047}{2199023255552}\cdot t^{79}-\frac{293548330004395296285}{549755813888}\cdot t^{77}+\frac{23368913861038978149801}{70368744177664}\cdot t^{75}-\frac{13369085605789883236683}{70368744177664}\cdot t^{73}+\frac{450375111060413511930147}{4503599627370496}\cdot t^{71}-\frac{109067491975584303452571}{2251799813685248}\cdot t^{69}+\frac{1555246871371194549895425}{72057594037927936}\cdot t^{67}-\frac{637410235896076506008673}{72057594037927936}\cdot t^{65}+\frac{240151431269242306594209}{72057594037927936}\cdot t^{63}-\frac{10389777204342045874023}{9007199254740992}\cdot t^{61}+\frac{3379688476168454609717613}{9223372036854775808}\cdot t^{59}-\frac{984316133857406441078115}{9223372036854775808}\cdot t^{57}+\frac{4199888358150758491587117}{147573952589676412928}\cdot t^{55}-\frac{511986796593129529329123}{73786976294838206464}\cdot t^{53}+\frac{3645598623170639319252081}{2361183241434822606848}\cdot t^{51}-\frac{738873728746810103849805}{2361183241434822606848}\cdot t^{49}+\frac{544360352131974593267325}{9444732965739290427392}\cdot t^{47}-\frac{22720679344956807453645}{2361183241434822606848}\cdot t^{45}+\frac{438838223542986242873205}{302231454903657293676544}\cdot t^{43}-\frac{59653390211790195475655}{302231454903657293676544}\cdot t^{41}+\frac{232901069790772709808405}{9671406556917033397649408}\cdot t^{39}-\frac{12699187651497933811225}{4835703278458516698824704}\cdot t^{37}+\frac{39424360100002110279795}{154742504910672534362390528}\cdot t^{35}-\frac{3384466003132862039035}{154742504910672534362390528}\cdot t^{33}+\frac{511086510709822648895}{309485009821345068724781056}\cdot t^{31}-\frac{2106590047824291323}{19342813113834066795298816}\cdot t^{29}+\frac{123266428787287191665}{19807040628566084398385987584}\cdot t^{27}-\frac{6047066370327715863}{19807040628566084398385987584}\cdot t^{25}+\frac{4030836746091804519}{316912650057057350374175801344}\cdot t^{23}-\frac{70399396970945757}{158456325028528675187087900672}\cdot t^{21}+\frac{64975338390996759}{5070602400912917605986812821504}\cdot t^{19}-\frac{1518907804863075}{5070602400912917605986812821504}\cdot t^{17}+\frac{112496587008949}{20282409603651670423947251286016}\cdot t^{15}-\frac{400629440323}{5070602400912917605986812821504}\cdot t^{13}+\frac{541037241719}{649037107316853453566312041152512}\cdot t^{11}-\frac{4015256741}{649037107316853453566312041152512}\cdot t^9+\frac{2491893615}{83076749736557242056487941267521536}\cdot t^7-\frac{3519151}{41538374868278621028243970633760768}\cdot t^5+\frac{151341}{1329227995784915872903807060280344576}\cdot t^3-\frac{61}{1329227995784915872903807060280344576}\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.