Rule: Q[14, 30]

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.

• $P_1$:
  $\frac{5014575}{2048}\cdot t^{14}-\frac{16900975}{2048}\cdot t^{12}+\frac{22309287}{2048}\cdot t^{10}-\frac{14549535}{2048}\cdot t^8+\frac{4849845}{2048}\cdot t^6-\frac{765765}{2048}\cdot t^4+\frac{45045}{2048}\cdot t^2-\frac{429}{2048}$
• $P_2$:
  $\frac{5014575}{2048}\cdot t^{44}-\frac{1258490082332805172340951579505461190751778798069480785816898225}{46251596947725885144840095835235901256000382845426498623488}\cdot t^{42}+\frac{17432444305309487031534066117286331198921269870879857837469401171}{123707182247170946226438749477120681099096914391363340496384}\cdot t^{40}-\frac{111743020900610231216238742902191688906873849362517891946965316815}{247414364494341892452877498954241362198193828782726680992768}\cdot t^{38}+\frac{2428055701979144365103884513043885454812160233803466812111072314438435}{2420207313483652391974047694770389005022732033152632393471256576}\cdot t^{36}-\frac{16950577562885448213865138052773954294175990001883487796216692942676735}{10340885793975605674798203786746207566915309596197611135740823552}\cdot t^{34}+\frac{242645399678999489568363804921988046569573363061066088216215292901345195}{118920186630719465260179343547581387019526060356272528061019470848}\cdot t^{32}-\frac{75311248392557571820637600801249808695350032920642036385481834451415611141}{38084189768487908749572434771112939193003220829096277111541485539072}\cdot t^{30}+\frac{76784905905073749778125927440029207331132968423687410310916747497662104395}{50778919691317211666096579694817252257337627772128369482055314052096}\cdot t^{28}-\frac{6666729509266622943417337671768538789434614301913109690412466495658688945}{7254131384473887380870939956402464608191089681732624211722187721728}\cdot t^{26}+\frac{7668638708751385939898482958534242810719948281446745598640589985763786575}{17228562038125482529568482396455853444453837994114982502840195839104}\cdot t^{24}-\frac{514026110214753051713780613016270681473001346653762063863608121309791925}{2996271658804431744272779547209713642513710955498257826580903624192}\cdot t^{22}+\frac{282592270203072814031313350628885392201269675941245866018331634171497990985}{5399281529165586003179548744071903983809707141807860603498788330793984}\cdot t^{20}-\frac{273972106319116599157256457045683766635480304427592842073556347090244587175}{21881298828723690644464487015449295092281444732589750866810879024796672}\cdot t^{18}+\frac{8037700121909255481834553091261918876740519585420237528454229074063621475}{3471044992598888245915533379017752210877818378506281598447820250317312}\cdot t^{16}-\frac{2026861504267915315654059063050310686513713842425136167356774418411030612325}{6246145464181699398525002315542445103474634172122053736406852540446002944}\cdot t^{14}+\frac{297839876654066034817366013013431816404586147003524592811204604554876425}{8889728467079451198754673283106130729015668631378123090420711674714112}\cdot t^{12}-\frac{22396929461371232685560342667835228661516348712584698032521023236983835}{9140143353476055457874523234742923143917518451980323740855097919072256}\cdot t^{10}+\frac{19457048936429310980563022237458156666652931266562124761970132979505825}{162237544524199984377272787416686885804535952522650746400177988063532544}\cdot t^8-\frac{166930568741042951061122928625442569050735847227287728050475125471525}{46353584149771424107792224976196253087010272149328784685765139446723584}\cdot t^6+\frac{37234385667786827260693180219463648148106423288762383870724413875625}{648950178096799937509091149666747543218143810090602985600711952254130176}\cdot t^4-\frac{1652254119533198896998607395208996954784366085766047694810460718375}{4542651246677599562563638047667232802527006670634220899204983665778911232}\cdot t^2+\frac{871905154070648013417324268816062303262163556496134443056778025}{2271325623338799781281819023833616401263503335317110449602491832889455616}$

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.