Rule: Q[1, 4, 6, 100]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{5}{4}\cdot t^3+\frac{5}{16}\cdot t$
• $P_3$:
  $t^{11}-3\cdot t^9+\frac{53}{16}\cdot t^7-\frac{13}{8}\cdot t^5+\frac{85}{256}\cdot t^3-\frac{5}{256}\cdot t$
• $P_4$:
  $t^{111}-28\cdot t^{109}+\frac{6103}{16}\cdot t^{107}-\frac{53901}{16}\cdot t^{105}+\frac{2775955}{128}\cdot t^{103}-\frac{6942715}{64}\cdot t^{101}+\frac{1797690415}{4096}\cdot t^{99}-\frac{6046578615}{4096}\cdot t^{97}+\frac{68990816895}{16384}\cdot t^{95}-\frac{21176668975}{2048}\cdot t^{93}+\frac{5797051436099}{262144}\cdot t^{91}-\frac{10897626635077}{262144}\cdot t^{89}+\frac{145129602367191}{2097152}\cdot t^{87}-\frac{107621081544281}{1048576}\cdot t^{85}+\frac{36585161295685045}{268435456}\cdot t^{83}-\frac{43676794389497689}{268435456}\cdot t^{81}+\frac{752604132482610687}{4294967296}\cdot t^{79}-\frac{183301116278487363}{1073741824}\cdot t^{77}+\frac{10362337555299118389}{68719476736}\cdot t^{75}-\frac{8314274908624560975}{68719476736}\cdot t^{73}+\frac{48547387259751207465}{549755813888}\cdot t^{71}-\frac{16134354132830447085}{274877906944}\cdot t^{69}+\frac{625536749805091941915}{17592186044416}\cdot t^{67}-\frac{345535829271272323755}{17592186044416}\cdot t^{65}+\frac{348157148318993025675}{35184372088832}\cdot t^{63}-\frac{4998816875193853257}{1099511627776}\cdot t^{61}+\frac{1072097324952290035227}{562949953421312}\cdot t^{59}-\frac{409204990999207013397}{562949953421312}\cdot t^{57}+\frac{1137602289161424394767}{4503599627370496}\cdot t^{55}-\frac{179763879349102610485}{2251799813685248}\cdot t^{53}+\frac{6604636170239675831835}{288230376151711744}\cdot t^{51}-\frac{1718972020997757832735}{288230376151711744}\cdot t^{49}+\frac{12956271044108553040495}{9223372036854775808}\cdot t^{47}-\frac{688873611257131211485}{2305843009213693952}\cdot t^{45}+\frac{8444242214178308490225}{147573952589676412928}\cdot t^{43}-\frac{1452170423536603721979}{147573952589676412928}\cdot t^{41}+\frac{1787663022090572784661}{1180591620717411303424}\cdot t^{39}-\frac{122587933455069648293}{590295810358705651712}\cdot t^{37}+\frac{954738115881781201789}{37778931862957161709568}\cdot t^{35}-\frac{102559686947916212805}{37778931862957161709568}\cdot t^{33}+\frac{38673276895465480499}{151115727451828646838272}\cdot t^{31}-\frac{397227569346242789}{18889465931478580854784}\cdot t^{29}+\frac{3613396028529247807}{2417851639229258349412352}\cdot t^{27}-\frac{220078587089850489}{2417851639229258349412352}\cdot t^{25}+\frac{90926563005389475}{19342813113834066795298816}\cdot t^{23}-\frac{1965865380999765}{9671406556917033397649408}\cdot t^{21}+\frac{35892487474964715}{4951760157141521099596496896}\cdot t^{19}-\frac{1036238159953815}{4951760157141521099596496896}\cdot t^{17}+\frac{378777221952255}{79228162514264337593543950336}\cdot t^{15}-\frac{1662974325975}{19807040628566084398385987584}\cdot t^{13}+\frac{1383366172461}{1267650600228229401496703205376}\cdot t^{11}-\frac{12640839783}{1267650600228229401496703205376}\cdot t^9+\frac{603441729}{10141204801825835211973625643008}\cdot t^7-\frac{1048509}{5070602400912917605986812821504}\cdot t^5+\frac{110935}{324518553658426726783156020576256}\cdot t^3-\frac{55}{324518553658426726783156020576256}\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.