Rule: Q[6, 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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{40}-\frac{283735305001382271902864159160819}{2025605911379235914031843553840}\cdot t^{38}+\frac{523185672247178821225836549752691907}{834144514305969349398313175471312}\cdot t^{36}-\frac{176379937773649529264151270064859099881}{102599775259634229975992520582971376}\cdot t^{34}+\frac{3695342650718641312280338319615088579377}{1145697490399248901398583146509847032}\cdot t^{32}-\frac{57824716703656600835711860983039983063369}{13175521139591362366083706184863240868}\cdot t^{30}+\frac{640655636730276577492068089232549407957981}{143113419274871694666081636145928305980}\cdot t^{28}-\frac{96698987362526025654109440491718486823467}{27714027224657693252796761285401989412}\cdot t^{26}+\frac{6865537627712728847808290079053046655574055}{3270255212509607803830017831677434750616}\cdot t^{24}-\frac{139119746177319058136562675900117827288635}{142185009239548165383913818768584119592}\cdot t^{22}+\frac{319142049202020722218256146167831668145}{905637001525784492891170820182064456}\cdot t^{20}-\frac{733287519214243246550734689889821527029401}{7535805489696052765347432394734958338376}\cdot t^{18}+\frac{38272497844614678940667647616205825406225}{1883951372424013191336858098683739584594}\cdot t^{16}-\frac{579559697234657143811135267097582411972405}{184627234497553292751012093671006479290212}\cdot t^{14}+\frac{9179529390091702460171320428792870011265}{26375319213936184678716013381572354184316}\cdot t^{12}-\frac{2093967628911044140608111241337322286675}{79125957641808554036148040144717062552948}\cdot t^{10}+\frac{5850266736939017643511741491095852799603}{4536554904797023764739154301630444919702352}\cdot t^8-\frac{315950720627457146142186972060107868204795}{8741941301543864794652350339241867360266432304}\cdot t^6+\frac{4195044114383943537908642204214007846805}{8741941301543864794652350339241867360266432304}\cdot t^4-\frac{17007575164676907737386744094888955405}{8741941301543864794652350339241867360266432304}\cdot t^2+\frac{5464104129008732590516403869398525}{30596794555403526781283226187346535760932513064}$

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.