Rule: Q[9, 14, 26]

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.

• $P_1$:
  $512\cdot t^9-9216\cdot t^7+48384\cdot t^5-80640\cdot t^3+30240\cdot t$
• $P_2$:
  $512\cdot t^{23}-\frac{847253248}{18099}\cdot t^{21}+\frac{10526171264}{6033}\cdot t^{19}-\frac{69724285120}{2011}\cdot t^{17}+\frac{2436061827136}{6033}\cdot t^{15}-\frac{5743770803680}{2011}\cdot t^{13}+\frac{24755471460720}{2011}\cdot t^{11}-\frac{63531751923640}{2011}\cdot t^9+\frac{92322361281150}{2011}\cdot t^7-\frac{70208873169435}{2011}\cdot t^5+\frac{50216778386775}{4022}\cdot t^3-\frac{12961617443775}{8044}\cdot t$
• $P_3$:
  $512\cdot t^{49}-\frac{2687276332023929663795686490499335529569343342061942969064554193980565218613076062332636457849802207395924631172736}{13423746162173595341629052375822682190056805916938167382709861175241526604500687539895039846171182794464646051}\cdot t^{47}+\frac{73199628484905869711152646609014240183182035985822278685428548559525238594557923398803563577664115980234873942299470912}{2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803}\cdot t^{45}-\frac{2627643089701331501207951926732904619769360832556808695075780134168836492845381375435234298390177595326052752630015416160}{684611054270853362423081671166956791692897101763846536518202919937317856829535064534647032154730322517696948601}\cdot t^{43}+\frac{575395585999715717709126750033219544041151085711989694855465128960976413838349940799155170151060109208666439653761826224336}{2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803}\cdot t^{41}-\frac{90703800267463748320914064194411716769648330632431882721421424216178182023770045013128744148303794980640283492210819846516248}{6161499488437680261807735040502611125236073915874618828663826279435860711465815580811823289392572902659272537409}\cdot t^{39}+\frac{1185743924332657425782833112910294296124129229309118184143785754814608013901366812353660979198201629514492009053343015153971956}{2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803}\cdot t^{37}-\frac{11838645150566807932214424948385453377495773894659766823018340252632750469993716406896780575305567091343400023272861141745412222}{684611054270853362423081671166956791692897101763846536518202919937317856829535064534647032154730322517696948601}\cdot t^{35}+\frac{824671142364804732598950646306120857270160786728859611354282631577448061078058194711786768386473550609942041117205795233928394535}{2053833162812560087269245013500870375078691305291539609554608759811953570488605193603941096464190967553090845803}\cdot t^{33}-\frac{4994827992012840526803887097043961922506022656350249844866186654191719881384747425303408765145170302661677093350315583602652141375}{684611054270853362423081671166956791692897101763846536518202919937317856829535064534647032154730322517696948601}\cdot t^{31}+\frac{47597132478042263984967309152762330603466478553737523490598308355477380256667320158842038797565219861112045196871910999128930224865}{456407369513902241615387780777971194461931401175897691012135279958211904553023376356431354769820215011797965734}\cdot t^{29}-\frac{3217411420615447543809440231647493970980685197566784460084475598206476776224100936710738474379451699233984575251204295465629276415715}{2738444217083413449692326684667827166771588407055386146072811679749271427318140258138588128618921290070787794404}\cdot t^{27}+\frac{2114066654187450609791323855241157728710091928507330429117110526085094910332663705538455659359978803148939656106786620493587507564765}{202847719783956551829061235901320530871969511633732307116504568870316402023565945047302824342142317783021318104}\cdot t^{25}-\frac{29416036275805506407892898257229914783003941200104355217998430553853388756537854798759870974179417576463648658064123554726760464450125}{405695439567913103658122471802641061743939023267464614233009137740632804047131890094605648684284635566042636208}\cdot t^{23}+\frac{318850757983765116497309075631008207686466428147908841610249739714412332342631767990210282770048588110884923120105289389963826548873625}{811390879135826207316244943605282123487878046534929228466018275481265608094263780189211297368569271132085272416}\cdot t^{21}-\frac{2665467255432820263873594786503331672003234676437351683111491457526838762985789059666800220418798244337782669857483833363416068381105625}{1622781758271652414632489887210564246975756093069858456932036550962531216188527560378422594737138542264170544832}\cdot t^{19}+\frac{498495083336450384532419303485513648914925999141413785775007420955116543843842329065891962735468345626534484260329374152748683178894375}{95457750486567789096028816894739073351515064298226968054825679468384189187560444728142505572772855427304149696}\cdot t^{17}-\frac{9467186302601486795926326189148784613386567781173741233608786625706146152423498584751800737223724466832950155722687838937841945820170625}{763662003892542312768230535157912586812120514385815744438605435747073513500483557825140044582182843418433197568}\cdot t^{15}+\frac{32742809911466960393632018258254467244403135803077010097500349930394096699241971232210467935599207032396734837288493503028733585793828125}{1527324007785084625536461070315825173624241028771631488877210871494147027000967115650280089164365686836866395136}\cdot t^{13}-\frac{79779796483547503935763109170043481546749990924885439814441715387405927352293864870681625042366184114855537395102320154534375252003268125}{3054648015570169251072922140631650347248482057543262977754421742988294054001934231300560178328731373673732790272}\cdot t^{11}+\frac{130734733531873512122844046379557769357154540501967210516601076351710357886824124153044123531705985234257369786830959512387992480201445625}{6109296031140338502145844281263300694496964115086525955508843485976588108003868462601120356657462747347465580544}\cdot t^9-\frac{134719215476321992952514769168067402388773071924540825301576284455540702294133764869296528325820365745016839768716081357992715882509513125}{12218592062280677004291688562526601388993928230173051911017686971953176216007736925202240713314925494694931161088}\cdot t^7+\frac{78674745079800699706859298489814672507510339102104231501021947234636566742817779373846973739139495639187669511233562443941971792509460625}{24437184124561354008583377125053202777987856460346103822035373943906352432015473850404481426629850989389862322176}\cdot t^5-\frac{21553872588401710738228946401522692571865352665061919994616822027148734401698840062096271251004928953316099559373326267790535504914340625}{48874368249122708017166754250106405555975712920692207644070747887812704864030947700808962853259701978779724644352}\cdot t^3+\frac{1685186845127382673824269330494937470004866243534082482931040765862865430004991700089068725149736818561694734479541907437747976425034375}{97748736498245416034333508500212811111951425841384415288141495775625409728061895401617925706519403957559449288704}\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.