Rule: Q[5, 34]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{39}-\frac{32875775023365787751569877}{425640654325582284781624}\cdot t^{37}+\frac{6500272104608694611183578795903}{18585599171126550464989611960}\cdot t^{35}-\frac{248727326474639924294327589471827}{256481268561546396416856645048}\cdot t^{33}+\frac{85060909300940386977433774743239}{46194206972106474623466116178}\cdot t^{31}-\frac{117182223983166103193921483684459}{46194206972106474623466116178}\cdot t^{29}+\frac{1089588261062184872189132420064653}{415747862748958271611195045602}\cdot t^{27}-\frac{9721568022914764778435969808796283}{4696411042164158253385721811430}\cdot t^{25}+\frac{139955817807514382379546877829677885}{110835300595074134779903034749748}\cdot t^{23}-\frac{8630237939873095343878979612673245}{14456778338487930623465613228228}\cdot t^{21}+\frac{1051547219034026195564873167423045}{4818926112829310207821871076076}\cdot t^{19}-\frac{15627798866346068051600975574573205}{255403083979953441014559167032028}\cdot t^{17}+\frac{4972696953940032800229208179272191}{383104625969930161521838750548042}\cdot t^{15}-\frac{260396620555213921014739805888065}{127701541989976720507279583516014}\cdot t^{13}+\frac{1380254359982633990995151241386585}{6001972473528905863842140425252658}\cdot t^{11}-\frac{961160738653200491231548293410125}{54017752261760152774579263827273922}\cdot t^9+\frac{6375801715863764995558743492657875}{7226374858128802660065937072004200232}\cdot t^7-\frac{1063823885373812792574498709790377}{42325909883325844151814774278881744216}\cdot t^5+\frac{42878778841145746046086618720465}{126977729649977532455444322836645232648}\cdot t^3-\frac{57370736999979889022542071935}{42325909883325844151814774278881744216}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.