Rule: Q[2, 5, 56]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^7-\frac{53}{3}\cdot t^5+\frac{215}{3}\cdot t^3-55\cdot t$
• $P_3$:
  $t^{63}-\frac{132241758327172913571480649746204622067465342066809609413991488490560585241588303653481303687}{74391046964816111147005084077851189236366973338259764854688931549778227355550752630201141}\cdot t^{61}+\frac{404070259569620935274153163216248911211572318711889796530648327963689068303502205677905376143773}{273702908644134748559735686701527960397953958508691587672912106645410459138347108733758915}\cdot t^{59}-\frac{55262629917905635529343805359215355025157302246821197978583826817495182178693334492992720518117033547}{72531270790695708368329956975904909505457799004803270733321708261033771671661983814446112475}\cdot t^{57}+\frac{6629764094453821937192375744349477513429847285509574368767796886796525466176212883951193842754162213409}{24177090263565236122776652325301636501819266334934423577773902753677923890553994604815370825}\cdot t^{55}-\frac{742186474078914706232685825905724761171659585359104310496770185250977500572779258366651533423853280067}{10137144764597583279990210618575109644368665129951540284181929875755942931049892916065145}\cdot t^{53}+\frac{11745110244392451724687493733746797026124481279246955575275355578857378879708411004657253536018414284139}{779780366507506406153093124505777664951435779227041560321686913519687917773068685851165}\cdot t^{51}-\frac{381798868116702784717215365034726418260218261245245716113146532391177105002990259451517255059157456065465}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{49}+\frac{49880297024474190390023052570197715024491143531003755980667344676649593586456189943133848479280706423890061}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{47}-\frac{5301740054219816749189332576857918306529609262961856629029117821353383682592987253851003782713931122588601631}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{45}+\frac{462346728158472683479989959595983554684750846412505421823392428131054355129896153625397355516281900776807584595}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{43}-\frac{33270142508078028578280967694624883650153258267869322462216770240874126230924333725445106439207482285570159868045}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{41}+\frac{1982517659804181371111357952838511668434471650714614231782643567954286825443185038565234727867592118151694821790325}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{39}-\frac{97996527807453414725829139763081852466192308020823456645730266660649645294504004246186331400002209472986932867411135}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{37}+\frac{4018894110249669903001997883860923893023020952107333437275599951309408027498412986775311923692675174098896334252474635}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{35}-\frac{136567256242003586615438632747562976448663013860479806791247022571822359846495337981544912255115106060147281399130807725}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{33}+\frac{3835009254396320213481537439953300049120026025577092214068913838453077590592247603507448030305632285939007791693362286475}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{31}-\frac{88631955754389911083822328857627418987933134731602376293226194670960982906700202674805947842241012514199378357458861305625}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{29}+\frac{1676481202800241810885987343099128999424484726020062336261100192416345135678698214537534942530392751298689016529551363581525}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{27}-\frac{25767074390494222576591549154267605093672335595050421890626569392109219300013201461678501899041790708941287862904772146517275}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{25}+\frac{318901068937789226542403265558404839921034521612001565754705731016005027602486555759595630726272536599079286596494800766181875}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{23}-\frac{3142520137825831960428370910871635976380963429941011160009404726352160787343045635705645654397387504581874593736362380906675625}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{21}+\frac{24313605301162835154703219740454593262682469791998885140368066688022540304862669755062585363871153602660552679019604129794178125}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{19}-\frac{145127036740661796107855582318037283894901476141521636933476474461898162938389735281915511056846658092737042028634729981555316875}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{17}+\frac{653523974318826132254880252514494938679655551035473371367876111801266654334613506518287106441998668422497851743074775131463579375}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{15}-\frac{2156154766371653354822487331555961702786615915231439180343195244457476679945175081930737359358716419338436333794179370473834503125}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{13}+\frac{5009007623958397126159520802993853480884973489712706786785621578034580618232459586577016077835839650765934491948215082292216440625}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^{11}-\frac{7742334892374730065770789134277527266691537122972126731372737846516403808218886205634192536879220391127381435471275309705213759375}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^9+\frac{7303318289168785714324427873732906068800474517188726667503394406476991646707449556913865748075070335027418177818777220874198674375}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^7-\frac{3635745673965389433026492020431681979659082318826777169796935546225309145246669586082669127364438577838997501482703736458378743125}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^5+\frac{715001641419277924030652236977470670409266978907096612713371595148328628141717939783901657687363612247124341845673649667977965625}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t^3-\frac{22954970122348436533368188744291437619925408573321481649396816859331442516032447491718434990386186985403263496503707599655559375}{155956073301501281230618624901155532990287155845408312064337382703937583554613737170233}\cdot t$

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 Hermite (probabilists') type can be downloaded here packed into a single file.