Rule: Q[2, 4, 21]

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.

• $P_1$:
  $\frac{1}{2}\cdot t^2-2\cdot t+1$
• $P_2$:
  $\frac{1}{2}\cdot t^6-\frac{162}{13}\cdot t^5+101\cdot t^4-\frac{4208}{13}\cdot t^3+\frac{5436}{13}\cdot t^2-\frac{2928}{13}\cdot t+\frac{552}{13}$
• $P_3$:
  $\frac{1}{2}\cdot t^{27}-\frac{2107742642895019151354087032446706788605995066775852893973961656307599104456761674635045430008550275981809551}{7161030798044942153187404556490143102801056175870963960646219345244978627715977424778577335372683571682374}\cdot t^{26}+\frac{571314877897894113773277938841628099022315107866313176099989435432870001996440097477863056516633341823408116349}{7161030798044942153187404556490143102801056175870963960646219345244978627715977424778577335372683571682374}\cdot t^{25}-\frac{94755674414245602837617805326885354251034458630386171532203270506199514377919439895508295246263903516317472752109}{7161030798044942153187404556490143102801056175870963960646219345244978627715977424778577335372683571682374}\cdot t^{24}+\frac{91624114674411681257817536043551560876470464849391615210141709363189019703200986155925326146129305081442282836099438}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{23}-\frac{7595960272591846634198770057752285217650560916735827512472071170457810448680357622852528023932092386364229445439826614}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{22}+\frac{476024303187980002466544326320460699826175704848210188834071233498901353714319667716857915417118433636922080133623141386}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{21}-\frac{23087518830329745563759074396936245055600159763816229483392923922077830692043569217003295790741811865964352169615407776130}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{20}+\frac{880216485078692334984775414248364295569446082601466882209392757533663090132845321280927333118875475675673727520619781505280}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{19}-\frac{26650166018047684841983907448047840700228659567973039504597661284620808039344427237247940024055199357033429375530183997928160}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{18}+\frac{644841219575933053446019632575867726448699199451994153619999665839038935818617308432004586634195076808517736788062514724823280}{60868761783382008302092938730166216373808977494903193665492864434582318335585808110617907350667810359300179}\cdot t^{17}-\frac{735915150304861830207535770519946268013507598091542958772901849664119492403542784747427021912985750241008540640745337397781360}{3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187}\cdot t^{16}+\frac{11456580163409518187335359947662423349900514379053709511809790385079371045137636917068033059933873009186426487015018641677593600}{3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187}\cdot t^{15}-\frac{142903077068457564617894778554337527702651281731281685988670804458966512930431571856975669678935968760273119957970915154217241600}{3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187}\cdot t^{14}+\frac{1423031858466719220218481840505344233744061294942573087274655073403864934496268779613193169892579988333145166598805549943169203200}{3580515399022471076593702278245071551400528087935481980323109672622489313857988712389288667686341785841187}\cdot t^{13}-\frac{865201713605469805645653688324191243371619267355508345761940813668928869761185779647474889125006162721027975587593255034574003200}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^{12}+\frac{5384125675116576789102444493554813690139070273682396310739227067196119706832753656960309241543954679569635122480679122401230028800}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^{11}-\frac{26098151011235107265614053320272248423350244118321222826305932301999681061964319209791761661647927530859544805223878512892598272000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^{10}+\frac{97189868840324065894215123289342898984549898960214902929540703366745674031160992567100117830183390162419157597863103308857398272000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^9-\frac{273259476999235619969979341101140332007084328406766602750039568426350960884384750921784984054219821998315659910423516341479855104000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^8+\frac{567468589400340337794907387655041328297271502625141911800959361011455587715038620163309595444136887234483030009140914306190876672000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^7-\frac{846725866268912041424810528130366470100405571409037501856873140115144134758807340957536080593105665046355926488909912809370001408000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^6+\frac{876694950132921721699027848529402609044792431988310289194971966329323465702506518958391747261609742718180295009223156741384232960000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^5-\frac{602255297607819882878262170851815924489218721847488786735727667778312653596551061971380470732723081163603543730799793591613480960000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^4+\frac{258280935610501654864394565297147502158215289195282930956611399829081875972039679027859685770127871329249094515227967379067371520000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t^3-\frac{401108029116655448590632837275528786784893374858119592663970846787634319555373166398004886019926882424851956423629348748001280000}{1754294659001700674470211797278330010485315084730760401922150746017878154756486385296074800434268390907}\cdot t^2+\frac{7286009829899536808405541736027886156319152563448789165009841343481020691168765028332840714057806662448980229986928030611210240000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}\cdot t-\frac{241068167028784022903912219647334839532208794188377200222687830549756409775208043157918876057900388769873641943421237239808000000}{275424261463267005891823252172697811646194468302729383101777667124806870296768362491483743668180137372399}$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.