Rule: Q[1, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{39}-\frac{4696539289052255393081411}{478845736116280070379327}\cdot t^{37}+\frac{6500272104608694611183578795903}{146361593472621584911793194185}\cdot t^{35}-\frac{35532475210662846327761084210261}{288541427131739695968963725679}\cdot t^{33}+\frac{48606233886251649701390728424708}{207873931374479135805597522801}\cdot t^{31}-\frac{66961270847523487539383704962548}{207873931374479135805597522801}\cdot t^{29}+\frac{622621863464105641250932811465516}{1870865382370312222250377705209}\cdot t^{27}-\frac{5555181727379865587677697033597876}{21133849689738712140235748151435}\cdot t^{25}+\frac{39987376516432680679870536522765110}{249379426338916803254781828186933}\cdot t^{23}-\frac{17260475879746190687757959225346490}{227694258831184907319583408344591}\cdot t^{21}+\frac{300442062581150341589963762120870}{10842583753865947967599209921171}\cdot t^{19}-\frac{4465085390384590871885993021306630}{574656938954895242282758125822063}\cdot t^{17}+\frac{2841541116537161600130976102441252}{1723970816864685726848274377466189}\cdot t^{15}-\frac{1041586482220855684058959223552260}{4022598572684266695979306880754441}\cdot t^{13}+\frac{5521017439930535963980604965546340}{189062132916160534711027423395458727}\cdot t^{11}-\frac{3844642954612801964926193173640500}{1701559196245444812399246810559128543}\cdot t^9+\frac{6375801715863764995558743492657875}{56907702007764320948019254442033076827}\cdot t^7-\frac{1063823885373812792574498709790377}{333316540331191022695541347446193735701}\cdot t^5+\frac{42878778841145746046086618720465}{999949620993573068086624042338581207103}\cdot t^3-\frac{57370736999979889022542071935}{333316540331191022695541347446193735701}\cdot t$

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.