Rule: Q[1, 2, 8, 32]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{11}-\frac{10483}{3705}\cdot t^9+\frac{3234}{1105}\cdot t^7-\frac{139986}{104975}\cdot t^5+\frac{68299}{272935}\cdot t^3-\frac{3633}{272935}\cdot t$
• $P_4$:
  $t^{43}-\frac{2545555631407969982800797042028162727747469858220247744154781970983638747056845333469}{235696089923868993790161758858300849142200056672964320600250264450781374059279048359}\cdot t^{41}+\frac{55969833676064724813058857147005319341079237235914033297564604489710622358268433861197444814}{1031058437774213010059907368169608522093782702917299244573809788096554390356667679022654475}\cdot t^{39}-\frac{4979722060816084557879741382346088988635190189486414776923430537752151327720328745621394258322}{29538919805005085007505767231946854676827143050244730989281252350204795078112952979719206275}\cdot t^{37}+\frac{219105140824583331644262067363353220793332697246202598263901426620587227599637151472233734303669}{604940891897021946386590712489870517011733956987888668890074962514468063586011845269591964125}\cdot t^{35}-\frac{2451240863933983211551289143092499334193837821189164418050890591998559594254847516405686893077041}{4291521856634167454954284701545787314800889130161139615773120028190873439321942855265458286675}\cdot t^{33}+\frac{6499146489777309383372769823495799212036209668840667556232714337245882749143174789243094847898952}{9493366531342249218535235854934620423650451712174642180346598850240417002136419043466013785675}\cdot t^{31}-\frac{235874261001474628399518697277724097288498450926167114546939624130406830049624226559518321634401032}{370241294722347719522874198342450196522367616774811045033517355159376263083320342695174537641325}\cdot t^{29}+\frac{6318048655932368878686307529619885516659400324834800457173369269012351400852652100598630972340263966}{13550831386837926534537195659333677192718654773958084248226735198833171228849524542643388077672495}\cdot t^{27}-\frac{15384165529876826230518548243516751337675485764889405830550263314263882415842020352134155907329793186}{56944376910501258229180523069849498174529959520194228678445682103358767984481620229056972691073875}\cdot t^{25}+\frac{12297686303990263818540786087959829218790674443247470394658331008174560738440113898328981452579436}{99033698974784796920313953164955648999182538295989962919035968875406553016489774311403430767085}\cdot t^{23}-\frac{4179939499181262892758079324122827249136806347449269968591954444407715115048876246039346988581604}{92539685927257924991113038203319212999236142342154555514509020096691369212129789110655664815145}\cdot t^{21}+\frac{267368579185683935291420824983776426808583418371019869838801965385767205198276180888246150400906898}{20698043085730022556345616211475730640829150503861902250078517494959969580446362831083317030320765}\cdot t^{19}-\frac{1970158008683610136471062726325695872699988798463157667355571370545095475750827694590412155340982}{685900063269805815707359601549878013438782765235189743179989858507445385706799548008608946423885}\cdot t^{17}+\frac{55877301473130124156158670346783058379341180355968984474991313605824593752519438893797444584709672}{114383922315876440442962615905523774594055831731868407171486544051094568734045689329670962535983175}\cdot t^{15}-\frac{22248982503359009832593899357907305708211026343058724561754127980003782653158838321515243134219352}{358402956589746180054616196503974493728041606093187675803991171360096315366676493232969015946080615}\cdot t^{13}+\frac{25004946509767669789190505161809275368810256755393924735156482900512497776896478721636794828322057}{4383543853674587894514151941856303423289124259139756957910353557404254934100120186464774887340524445}\cdot t^{11}-\frac{802987936330933173503827209758725300889867738231357889742037012256526385461682051568381784098361}{2220236497315700362156518516005140694912673326057798978681867386217739512076684250287353514367278615}\cdot t^9+\frac{2683024703606595583510122726396158785497315281419280566099258601934565551038672672627651918}{181792884411340404663597684107519912790688064034864405034133086564950422670652931326238722211355}\cdot t^7-\frac{7276237995770625380244939422274373646697892349519347922671846076418506303136947411873368672546}{20968900252426058975922674873381884340841914746101434798662080869834206502946462363825005413468742475}\cdot t^5+\frac{11972974087960658737695634254822190901481371973757364037175367452450269440329198174599085309903}{3107591017409541940231740416235195259312771765372232637161720384909429403736665722318865802276067634795}\cdot t^3-\frac{13229526470654654444993786528808421155004757073394751660114606304263425241824510878574291247}{1035863672469847313410580138745065086437590588457410879053906794969809801245555240772955267425355878265}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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