Rule: Q[2, 13, 16]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{15}-\frac{9527}{1738}\cdot t^{13}+\frac{347711}{43450}\cdot t^{11}-\frac{323869}{54510}\cdot t^9+\frac{42861}{18170}\cdot t^7-\frac{165711}{345230}\cdot t^5+\frac{252343}{5868910}\cdot t^3-\frac{32643}{29344550}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{31}-\frac{141391306262561311286950316776687011061921}{12070357394985361671465001778565391179542}\cdot t^{29}+\frac{1736825412824773909199578547798456969193641}{42017066881278157717125006191208640181950}\cdot t^{27}-\frac{289212473843083602412306804611634153144877679}{3319348283620974459652875489105482574374050}\cdot t^{25}+\frac{3768586091612495304355613356120007462620910942653}{30846438051827025975597399690218121125052096726}\cdot t^{23}-\frac{33668649524736075023137315178030679597447362659019}{280300241427471670821732892837199448484169052858}\cdot t^{21}+\frac{49835493640547136114062942900061639017241377614117013}{586107804824843263688243478922584046780397489526078}\cdot t^{19}-\frac{406719229048144691472933946200141776067563048615482979}{9285181539593569598429541429247252530573665491965762}\cdot t^{17}+\frac{6183482186049902577486407636797424428008638077355634527}{376940374879715422598138391576577082909963663309392686}\cdot t^{15}-\frac{260282375743498464186030259214968383156913973820635155}{58977065457370440270457027253478046985912682014394774}\cdot t^{13}+\frac{26446525423838885176945499405566356545064751341124597}{31756881400122544761015322367257409915491444161597186}\cdot t^{11}-\frac{8258095562280693337782198105979245176400292834412573}{77948708891209882595219427628722733428933544760284002}\cdot t^9+\frac{39288180909167129403542988393674605274865090114563}{4606897688605785023358122200279121361048081841624350}\cdot t^7-\frac{1947391835037406771130959133277109626395323604933723}{4980056401382853610250130098501730191292976470795922350}\cdot t^5+\frac{176037276900766718278259848231829292694248567908287}{20916236885807985163050546413707266803430501177342873870}\cdot t^3-\frac{53044455882306252086420206333004502184765158145}{981255557605806711352988597186266837691801289801270626}\cdot t$

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.