Rule: Q[2, 4, 29]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{35}-\frac{1348884798795788104131608927}{104818316823828572099222066}\cdot t^{33}+\frac{84604034837056929232862290223999}{1678403298141555010738793331825}\cdot t^{31}-\frac{157614610791101210228199503495083}{1320343927871356608447850754369}\cdot t^{29}+\frac{10254864782950919396564121670655819}{53756859920476661915376780713595}\cdot t^{27}-\frac{2782789929759671256838073312062671}{12799252362018252836994471598475}\cdot t^{25}+\frac{34592513659250395791590409548817459}{189940905052350872100997958521369}\cdot t^{23}-\frac{5691457639581010024778697956192169}{49984448697987071605525778558255}\cdot t^{21}+\frac{71018080600283032723162678712040780}{1329586335366456104706985709649583}\cdot t^{19}-\frac{7073864972766194084692257668033556}{377423558529390904614838911539873}\cdot t^{17}+\frac{560067296264190313595446526546136381}{115114185351464225907525868019661265}\cdot t^{15}-\frac{129521395024303765904165442225209513}{141425999146084620400674637852726697}\cdot t^{13}+\frac{501735618684943514152754848938130893}{4141761403563906740305471537115567555}\cdot t^{11}-\frac{62252941431212107481289049646987875}{5798465964989469436427660151961794577}\cdot t^9+\frac{127081029023077329336679620550175373}{214543240704610369147823425622586399349}\cdot t^7-\frac{19356005636071440906599546500625301}{1072716203523051845739117128112931996745}\cdot t^5+\frac{731879907174040061970107041731951}{3003605369864545168069527958716209590886}\cdot t^3-\frac{13158428421977335689969135190623}{15018026849322725840347639793581047954430}\cdot t$

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.