Rule: Q[2, 4, 24]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{30}-\frac{5976898516713017708468405}{562075502299892163741454}\cdot t^{28}+\frac{4130099124017197361162852025}{121970383999076599531895518}\cdot t^{26}-\frac{6501903630552375566242425879825}{101601329871230807410068966494}\cdot t^{24}+\frac{381516935947208721481097940823575}{4775262503947847948273241425218}\cdot t^{22}-\frac{47347730144552188796555760732225}{682180357706835421181891632174}\cdot t^{20}+\frac{1262792729297189609782606751726175}{29333755381393923110821340183482}\cdot t^{18}-\frac{25694773441101670440826585426275}{1334832375845894392390316256962}\cdot t^{16}+\frac{62552910884951418179666887658475}{10106587988547486113812394516998}\cdot t^{14}-\frac{3692684928100209137907621136293825}{2617606289033798903477410179902482}\cdot t^{12}+\frac{4061050124842197067196509858971435}{18323244023236592324341871259317374}\cdot t^{10}-\frac{419489792361774637415641412233875}{18323244023236592324341871259317374}\cdot t^8+\frac{116632356084481638420889735106475}{81145794960047766007799715576976942}\cdot t^6-\frac{3874480752150145266522998348475}{81145794960047766007799715576976942}\cdot t^4+\frac{967920273805290853377107475}{1531052735095240868071692746735414}\cdot t^2-\frac{16201434640010468831825537}{11592256422863966572542816510996706}$

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.