Rule: Q[5, 10, 34]

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.

• $P_1$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_2$:
  $t^{15}-\frac{1805}{21}\cdot t^{13}+\frac{169685}{63}\cdot t^{11}-\frac{2447225}{63}\cdot t^9+268675\cdot t^7-846835\cdot t^5+1039225\cdot t^3-327525\cdot t$
• $P_3$:
  $t^{49}-\frac{4175800205808505672520320090786198999805978345308978443685245435150381643997343295853489}{4590629804181073661263159751716754087714196155258679218560831995805786188647872427496}\cdot t^{47}+\frac{1639633442027414667183921517477927533365639865733293557910836978694224563542005361199709720153}{4338145164951114609893685965372332612889915366719451861539986236036467948272239443983720}\cdot t^{45}-\frac{3224001978586333697225100349480918863501361774349694221876997003445050706332371000278738334502641}{33837532286618693957170750529904194380541339860411724520011892641084449996523467663073016}\cdot t^{43}+\frac{236744622419333190661335716380685164876887194671393693222072429147849178429133444756845441862551561}{14501799551408011695930321655673226163089145654462167651433668274750478569938628998459864}\cdot t^{41}-\frac{204913304471979855280122079027876331999195528039473245799213203871201803099814802953850243949393547175}{101512596859856081871512251589712583141624019581235173560035677923253349989570402989219048}\cdot t^{39}+\frac{6316533025430263551483970362931845268601710122239858784069040298489318324671947729402795692387733947005}{33837532286618693957170750529904194380541339860411724520011892641084449996523467663073016}\cdot t^{37}-\frac{9118187731350101871789057357350193072553957422696970314921971475049982440619167281652153329663607361551}{690561883400381509330015316936820293480435507355341316734936584511927550949458523736184}\cdot t^{35}+\frac{3502705545374631251376036636993091822085826256436846332138207398476869859612758763804464314050421287821165}{4833933183802670565310107218557742054363048551487389217144556091583492856646209666153288}\cdot t^{33}-\frac{25067979424138137839153374150874514976438182329410632715812941909067995730721847733387997460237504089338635}{805655530633778427551684536426290342393841425247898202857426015263915476107701611025548}\cdot t^{31}+\frac{845823351087858857131392077188279206277381522984991943535999708992932508774412080795127326786808437148569475}{805655530633778427551684536426290342393841425247898202857426015263915476107701611025548}\cdot t^{29}-\frac{3205634250434898003043614006112402984493730884283728105036220656315531643217682298473803555745498140168579975}{115093647233396918221669219489470048913405917892556886122489430751987925158243087289364}\cdot t^{27}+\frac{1330179635623195626049131204605440707400948836783403659056003712436407028024498971506436915444588391989345275}{2295314902090536830631579875858377043857098077629339609280415997902893094323936213748}\cdot t^{25}-\frac{7195269663505307303147833907171441634427250020847203123040057995535839181800642264815269256739327243315488125}{765104967363512276877193291952792347952366025876446536426805332634297698107978737916}\cdot t^{23}+\frac{12896858368647880770186691960140958643016749497321164262734706386020166701602750824595437156586933435110866875}{109300709623358896696741898850398906850338003696635219489543618947756814015425533988}\cdot t^{21}-\frac{41202187137980680290277682657151375631564035826849532330807614040520678758496402607458993471337691028977991875}{36433569874452965565580632950132968950112667898878406496514539649252271338475177996}\cdot t^{19}+\frac{127221201665247331790886152292500751388320140206688740326828652008171602840322668239284286840539684012099044375}{15614387089051270956677414121485558121476857670947888498506231278250973430775076284}\cdot t^{17}-\frac{9447119284826398906207668212197093454781066672534450982220901963909053216580797983806318632255270726235393354625}{218601419246717793393483797700797813700676007393270438979087237895513628030851067976}\cdot t^{15}+\frac{1709550630279463198340996190013364426054780341225152068435371517453887637624286058829132090403514989993405923125}{10409591392700847304451609414323705414317905113965258999004154185500648953850050856}\cdot t^{13}-\frac{31426373789790618575568913313928035074200404377195029518261909575910999869788663949923167981671865478150059650625}{72867139748905931131161265900265937900225335797756812993029079298504542676950355992}\cdot t^{11}+\frac{54245925137612520539265552783291583499632798397459586738346384885169279236529081016074534150271100401476833053125}{72867139748905931131161265900265937900225335797756812993029079298504542676950355992}\cdot t^9-\frac{2716809932920654938137836567477849613175758991348831697247691029853075398392163129876923655640419236839070940625}{3469863797566949101483869804774568471439301704655086333001384728500216317950016952}\cdot t^7+\frac{1521983973176400770096156310676939892621577306251042758179112904278014889618301667215480307033748794226530230625}{3469863797566949101483869804774568471439301704655086333001384728500216317950016952}\cdot t^5-\frac{331693360783493209857351330325205866213699516361766042363268026742383091397561171168445125333640941475310696875}{3469863797566949101483869804774568471439301704655086333001384728500216317950016952}\cdot t^3+\frac{4565967048866500492887700704482738760709333621071055677585247560936990098297633603659688510011099956590334375}{3469863797566949101483869804774568471439301704655086333001384728500216317950016952}\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.