Rule: Q[4, 76]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{80}-\frac{1473707549200388449227348966034232199462287822946710120047236592325209726974792}{490043382695627181161356879480214118047430836960720016993391789497172358057}\cdot t^{78}+\frac{4206440037223225671833823613663809736739265030444841798601029052128427728278234767}{980086765391254362322713758960428236094861673921440033986783578994344716114}\cdot t^{76}-\frac{1896649198069291907262194521172493457240619584736572972799092501994420553855433178175}{490043382695627181161356879480214118047430836960720016993391789497172358057}\cdot t^{74}+\frac{33261220892609449812581364014055726496748399882942736260015025413793179521041904397775}{13425846101250059757845393958362030631436461286595068958723062725949927618}\cdot t^{72}-\frac{8047239857488093811368224598825251484526703820991115777856947411054038557922347249896150}{6712923050625029878922696979181015315718230643297534479361531362974963809}\cdot t^{70}+\frac{6122436185951456269550323991067831129914052921900163983498133188391039731634293180953272425}{13425846101250059757845393958362030631436461286595068958723062725949927618}\cdot t^{68}-\frac{939998246644802473046832522702712447099847979568194919699115880960278067374153328894269422575}{6712923050625029878922696979181015315718230643297534479361531362974963809}\cdot t^{66}+\frac{474816642397771523551576430128383630571200492672216502445637600771730208017689776008546860348375}{13425846101250059757845393958362030631436461286595068958723062725949927618}\cdot t^{64}-\frac{50001750084743642888684283824151479010293428444887364738761060787412490416632744164749849683494000}{6712923050625029878922696979181015315718230643297534479361531362974963809}\cdot t^{62}+\frac{8873168251600781443988502790903506676978423584931299068974281116065910815790560665845957980779720750}{6712923050625029878922696979181015315718230643297534479361531362974963809}\cdot t^{60}-\frac{1337114087180430938171697926199333998297381776560953109310909485894632858956872847303675890036588739500}{6712923050625029878922696979181015315718230643297534479361531362974963809}\cdot t^{58}+\frac{5934985620563610851731107142850062293385740612626232387996329430511864466558355268274402572598327547750}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{56}-\frac{655448278028924999651267016888913518226425540334343324450100837590190467032100472083273639986777207005000}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{54}+\frac{62302271191911997966300518258473390956639008130962262804134599022517157718864043023242228852073551770541250}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{52}-\frac{5107913419239570433193124152442210983853929345803838811778924442489541633441597011792337005066146400225287500}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{50}+\frac{361653690106960322808601967570601716401360087424566980664484346331853303962400974079024601476624562773189662500}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{48}-\frac{22122519535556360064012862619344456308523853464362750992679665313408439106791654672308744437964175406056143300000}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{46}+\frac{1168753732086978639057459817454066870454231789880770933989267808633950385673723017722143477853516375999772836578125}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{44}-\frac{53271837743843954657998165086931370080880486413161562287302856698469303437693998059513279010039330967433968194406250}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{42}+\frac{2091156264738216678132511418110345744151430368076033041439153554814580098000577689680153193674651093164318225349953125}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{40}-\frac{70517971022588423745564598885309559100548087067935891037180144063771579674080087433373213165544787411220147519365812500}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{38}+\frac{2036176434716308258200851986982260271753562768195813702704136114997972207114403450497444366953355771971546308818159546875}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{36}-\frac{50136447397466696435943773414974189268434333790418798720059686671571354020525709115336374916685544904511244637855926406250}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{34}+\frac{1047468636034666010080308613135582046957072440908866307503203146940131090229091943230924528033794391498505175450512226640625}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{32}-\frac{18457028225955078295129380099402057949754689580372684797720975814131919598583183833019337247507856044199159220094428918250000}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{30}+\frac{272327237814115963864443590824521953339849127236043266587285117149510886113644454819906721669680123121243239513983677039968750}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{28}-\frac{3335864016726365136750690889676036787612058470178023568569697767461739216368044135773740123297007390396952520194552657015687500}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{26}+\frac{33580067637369765599964023669514030937781863069909036452340098501255875712490753334866675621070859514168552980482144657017968750}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{24}-\frac{274418505481136225111974467610377417142010237772029671169039192790046761299580855593195075729638444379705750365522935162778125000}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{22}+\frac{1794044938813658332902714967790407363963140152003000699596304928424407459372134376527728918379805233587885588944861395075716406250}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{20}-\frac{9217496544609049261938742374999685449792619092347411567606169814205362648103055251195819580150200104139613841899175057748610937500}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{18}+\frac{36413974866628094988427263879343113638633219779720743698065525557829443135636505370370232248287220375112921976381338625053276171875}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{16}-\frac{107643391646466629306873519665402214053818802119372596727417148251722296538650341417219846122604504013685207169921637119885046875000}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{14}+\frac{460061524379680383034127516586507077628724049723885833472107139103749292253154462350093619106545048766221248931247199982488810546875}{462960210387933095098117033046966573497809009882588584783553887101721642}\cdot t^{12}-\frac{339772833162290787385611417330940615415401256111634714284253387568641022498333904120868745191710566236123426116889456374900935546875}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^{10}+\frac{653210364613555708594205668385884183491456005203546282505334781085446314298462327716194735786005752987506852095097976175144107421875}{462960210387933095098117033046966573497809009882588584783553887101721642}\cdot t^8-\frac{187586976655628641232260737832786612155997674803122469458297045981220661690931218620055407794557264323449439471672423767934730468750}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^6+\frac{112646548841087133164737626610564006732865582827273084877577095232486145830717656052127541477101376942217352221607148193589658203125}{462960210387933095098117033046966573497809009882588584783553887101721642}\cdot t^4-\frac{6829350250911234817540290665403814366241727402151739105467317684049086972782596173754855620125852609691379588029922854081357421875}{231480105193966547549058516523483286748904504941294292391776943550860821}\cdot t^2+\frac{294230749355807293095389014929934664767560102406216575101992644807079566770235961352613211991262603831308661978472013028076171875}{462960210387933095098117033046966573497809009882588584783553887101721642}$

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.