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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{15}-\frac{28880}{21}\cdot t^{13}+\frac{1357480}{63}\cdot t^{11}-\frac{9788900}{63}\cdot t^9+537350\cdot t^7-846835\cdot t^5+\frac{1039225}{2}\cdot t^3-\frac{327525}{4}\cdot t$
• $P_3$:
  $32\cdot t^{49}-\frac{8351600411617011345040640181572397999611956690617956887370490870300763287994686591706978}{573828725522634207657894968964594260964274519407334902320103999475723273580984053437}\cdot t^{47}+\frac{1639633442027414667183921517477927533365639865733293557910836978694224563542005361199709720153}{542268145618889326236710745671541576611239420839931482692498279504558493534029930497965}\cdot t^{45}-\frac{3224001978586333697225100349480918863501361774349694221876997003445050706332371000278738334502641}{8459383071654673489292687632476048595135334965102931130002973160271112499130866915768254}\cdot t^{43}+\frac{236744622419333190661335716380685164876887194671393693222072429147849178429133444756845441862551561}{7250899775704005847965160827836613081544572827231083825716834137375239284969314499229932}\cdot t^{41}-\frac{204913304471979855280122079027876331999195528039473245799213203871201803099814802953850243949393547175}{101512596859856081871512251589712583141624019581235173560035677923253349989570402989219048}\cdot t^{39}+\frac{6316533025430263551483970362931845268601710122239858784069040298489318324671947729402795692387733947005}{67675064573237387914341501059808388761082679720823449040023785282168899993046935326146032}\cdot t^{37}-\frac{9118187731350101871789057357350193072553957422696970314921971475049982440619167281652153329663607361551}{2762247533601526037320061267747281173921742029421365266939746338047710203797834094944736}\cdot t^{35}+\frac{3502705545374631251376036636993091822085826256436846332138207398476869859612758763804464314050421287821165}{38671465470421364522480857748461936434904388411899113737156448732667942853169677329226304}\cdot t^{33}-\frac{25067979424138137839153374150874514976438182329410632715812941909067995730721847733387997460237504089338635}{12890488490140454840826952582820645478301462803966371245718816244222647617723225776408768}\cdot t^{31}+\frac{845823351087858857131392077188279206277381522984991943535999708992932508774412080795127326786808437148569475}{25780976980280909681653905165641290956602925607932742491437632488445295235446451552817536}\cdot t^{29}-\frac{3205634250434898003043614006112402984493730884283728105036220656315531643217682298473803555745498140168579975}{7365993422937402766186830047326083130457978745123640711839323568127227210127557586519296}\cdot t^{27}+\frac{1330179635623195626049131204605440707400948836783403659056003712436407028024498971506436915444588391989345275}{293800307467588714320842224109872261613708553936555469987893247731570316073463835359744}\cdot t^{25}-\frac{7195269663505307303147833907171441634427250020847203123040057995535839181800642264815269256739327243315488125}{195866871645059142880561482739914841075805702624370313325262165154380210715642556906496}\cdot t^{23}+\frac{12896858368647880770186691960140958643016749497321164262734706386020166701602750824595437156586933435110866875}{55961963327159755108731852211404240307373057892677232378646332901251488775897873401856}\cdot t^{21}-\frac{41202187137980680290277682657151375631564035826849532330807614040520678758496402607458993471337691028977991875}{37307975551439836739154568140936160204915371928451488252430888600834325850598582267904}\cdot t^{19}+\frac{127221201665247331790886152292500751388320140206688740326828652008171602840322668239284286840539684012099044375}{31978264758377002919275344120802423032784604510101275644940761657857993586227356229632}\cdot t^{17}-\frac{9447119284826398906207668212197093454781066672534450982220901963909053216580797983806318632255270726235393354625}{895391413234556081739709635382467844917968926282835718058341326420023820414365974429696}\cdot t^{15}+\frac{1709550630279463198340996190013364426054780341225152068435371517453887637624286058829132090403514989993405923125}{85275372689005341118067584322139794754092278693603401719842031087621316229939616612352}\cdot t^{13}-\frac{31426373789790618575568913313928035074200404377195029518261909575910999869788663949923167981671865478150059650625}{1193855217646074775652946180509957126557291901710447624077788435226698427219154632572928}\cdot t^{11}+\frac{54245925137612520539265552783291583499632798397459586738346384885169279236529081016074534150271100401476833053125}{2387710435292149551305892361019914253114583803420895248155576870453396854438309265145856}\cdot t^9-\frac{2716809932920654938137836567477849613175758991348831697247691029853075398392163129876923655640419236839070940625}{227400993837347576314846891525706119344246076516275737919578749566990176613172310966272}\cdot t^7+\frac{1521983973176400770096156310676939892621577306251042758179112904278014889618301667215480307033748794226530230625}{454801987674695152629693783051412238688492153032551475839157499133980353226344621932544}\cdot t^5-\frac{331693360783493209857351330325205866213699516361766042363268026742383091397561171168445125333640941475310696875}{909603975349390305259387566102824477376984306065102951678314998267960706452689243865088}\cdot t^3+\frac{4565967048866500492887700704482738760709333621071055677585247560936990098297633603659688510011099956590334375}{1819207950698780610518775132205648954753968612130205903356629996535921412905378487730176}\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 (physicists') type can be downloaded here packed into a single file.