Rule: Q[2, 7, 20]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^9-\frac{151}{50}\cdot t^7+\frac{1281}{650}\cdot t^5-\frac{651}{1430}\cdot t^3+\frac{56}{2145}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{29}-\frac{38088523035606372329691420071995395909967}{3604732953003583797206419381991952192725}\cdot t^{27}+\frac{146468851414009861237072608232395607584610683}{4404983668570379400186244484794165579509950}\cdot t^{25}-\frac{285016125197169696675353330136389057364661161}{4621844403023075001426182674814801423424286}\cdot t^{23}+\frac{26380817952866870779825969278716761372685501249}{352310593812258944426895833893837363049205801}\cdot t^{21}-\frac{86040532106595713981473723789209776587452609055}{1375688985362153973476450399014031608096898842}\cdot t^{19}+\frac{1642947863301094626569901870786672439323474688017}{44709892024270004137984637967956027263149212365}\cdot t^{17}-\frac{682538373671431110750890243469484851826545518039}{44709892024270004137984637967956027263149212365}\cdot t^{15}+\frac{556526278177143942362489037073832653910635038393}{125187697667956011586356986310276876336817794622}\cdot t^{13}-\frac{4271199445610653857980405813278119961235037042}{4814911448767538907167576396549110628339145947}\cdot t^{11}+\frac{1287156537900091641711675188488566447036004876265}{11045406863472734253042420253683659781410000802418}\cdot t^9-\frac{521366066708211213290885932854340011185466679959}{55227034317363671265212101268418298907050004012090}\cdot t^7+\frac{128342341542152663668766918112839610937709254}{303445243501998193764901655320979664324450571495}\cdot t^5-\frac{3932245356804471053630424567675419046805211}{458104432125597273167657982871672525496267314386}\cdot t^3+\frac{1294245696243053076702989441330254233945304}{26035601892471445025028562026540055199037859034271}\cdot t$

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.