Rule: Q[2, 81]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{83}-\frac{2292206499417318610029406910034475422563558127935399624882}{342864931300254940565947220714331861629247314127176641}\cdot t^{81}+\frac{1823208163888132696599251399068638637851551819096200375205580}{342864931300254940565947220714331861629247314127176641}\cdot t^{79}-\frac{11633238911113542573985440806560789192273040104670725852668810}{4340062421522214437543635705244707109230978659837679}\cdot t^{77}+\frac{8350529509712013846585409310276825024970791661285613188445737525}{8680124843044428875087271410489414218461957319675358}\cdot t^{75}-\frac{4546196339549181571666760112157710179465589239732547680693653496925}{17360249686088857750174542820978828436923914639350716}\cdot t^{73}+\frac{976268887464594805406817354507480360945853214531896029154183064177025}{17360249686088857750174542820978828436923914639350716}\cdot t^{71}-\frac{339706875681611190549608056780609878369003546874639261263941884447253625}{34720499372177715500349085641957656873847829278701432}\cdot t^{69}+\frac{390419321575490607135900652530078340150414854638604221944968520243981138875}{277763994977421724002792685135661254990782634229611456}\cdot t^{67}-\frac{93933715422881533025663615711480484307276520153543369048314858597697664211875}{555527989954843448005585370271322509981565268459222912}\cdot t^{65}+\frac{1195407427656661356344232624534932399662147949894638578437938526054278172321625}{69440998744355431000698171283915313747695658557402864}\cdot t^{63}-\frac{207670755595943637808363553830424357909355120191831426419174721621005867673906625}{138881997488710862001396342567830627495391317114805728}\cdot t^{61}+\frac{61946218604879692987939283628049721247910863446654452949766157268620705870541154375}{555527989954843448005585370271322509981565268459222912}\cdot t^{59}-\frac{7969687531105934022788051245462310985658804497441796073855489678591541416463483729375}{1111055979909686896011170740542645019963130536918445824}\cdot t^{57}+\frac{443819081478530184902856725490949208969334268142067149893999360287376369058662748015625}{1111055979909686896011170740542645019963130536918445824}\cdot t^{55}-\frac{42903231394718190920172658469064122483855551313065240434245345080608452860511785422230625}{2222111959819373792022341481085290039926261073836891648}\cdot t^{53}+\frac{28847309495189644645589163267907224289745689945165358956970495156516218531924795606940004375}{35553791357109980672357463697364640638820177181390266368}\cdot t^{51}-\frac{2110071941956384181038452363797195114108617877672157544105946066436990978221772829347233109375}{71107582714219961344714927394729281277640354362780532736}\cdot t^{49}+\frac{33591062638967901889742718880855357305943047154462915051838714936876004253636704473508109546875}{35553791357109980672357463697364640638820177181390266368}\cdot t^{47}-\frac{1861460203208036806516587568478144201528547780375964106534702594517136639713308424868070314921875}{71107582714219961344714927394729281277640354362780532736}\cdot t^{45}+\frac{179364807995206767040896126352869421190825146650047908571095985618101838914816832542279797323109375}{284430330856879845378859709578917125110561417451122130944}\cdot t^{43}-\frac{7501137402531169280175953587335310356503934710843640935596025818297307471414693633972687239164984375}{568860661713759690757719419157834250221122834902244261888}\cdot t^{41}+\frac{135851413869093795764240147000630299851771778520520042685469042934393486658719455551691395877675859375}{568860661713759690757719419157834250221122834902244261888}\cdot t^{39}-\frac{4249760757954426043650255520632825409007325419726539365758110814181937265079824221087162373646303984375}{1137721323427519381515438838315668500442245669804488523776}\cdot t^{37}+\frac{457624512520368068846682102495754945447101001653583303071234763774616217579619501490820959891448305859375}{9101770587420155052123510706525348003537965358435908190208}\cdot t^{35}-\frac{10555908825605517354986823044390137237766455384876993529730997606765890089902008643695012132134133492984375}{18203541174840310104247021413050696007075930716871816380416}\cdot t^{33}+\frac{25943976181266697242842015202275624887571763746396711286930619890612705280499954924075386063239177778078125}{4550885293710077526061755353262674001768982679217954095104}\cdot t^{31}-\frac{432143165534466398443553174300130054066143492344725851126122610261210892910820890013024092128100800248203125}{9101770587420155052123510706525348003537965358435908190208}\cdot t^{29}+\frac{12106728830466406208995544294493217150321313884877075228120318460894219540400134133675523970734279290788984375}{36407082349680620208494042826101392014151861433743632760832}\cdot t^{27}-\frac{141384081276278747895101528742524642040906473745060081776815914127547463393849942151642951506328483324393359375}{72814164699361240416988085652202784028303722867487265521664}\cdot t^{25}+\frac{681174981815596344579043555120570692863757638555453678962946765452393416924629235150893495455055172715151953125}{72814164699361240416988085652202784028303722867487265521664}\cdot t^{23}-\frac{5349150902716101105473955001023067690558537929727695422825126837018178315182006973049154033701689870597073828125}{145628329398722480833976171304405568056607445734974531043328}\cdot t^{21}+\frac{539598676927435525899779194028458393858398717880699039385190157572435797136519024605371195246272915948675451171875}{4660106540759119386687237481740978177811438263519184993386496}\cdot t^{19}-\frac{2681780092451980439664837039829199706533145848089039398573026713063989423381714279210284487851863503875046779296875}{9320213081518238773374474963481956355622876527038369986772992}\cdot t^{17}+\frac{2567457949916340426939909165147296826709134703523547411240977155070811534328739067283645509427585534197866220703125}{4660106540759119386687237481740978177811438263519184993386496}\cdot t^{15}-\frac{7359407422142101242644943871396181840655370676874166271726782791232900935827291566071019593009922693562056986328125}{9320213081518238773374474963481956355622876527038369986772992}\cdot t^{13}+\frac{30404577642985785219370694405185383871794461387103324675499414508097924830896252364594778183527384732965566345703125}{37280852326072955093497899853927825422491506108153479947091968}\cdot t^{11}-\frac{42986795633817177782893642213179339293906146160171786113785199026493612838551800095274754878936416540376271611328125}{74561704652145910186995799707855650844983012216306959894183936}\cdot t^9+\frac{19315704066634817524635379777255583148226507761107060935147556714276349017328383987167242601032145054157384853515625}{74561704652145910186995799707855650844983012216306959894183936}\cdot t^7-\frac{9837284035604774336966443568095897740535076341553261876845273470965227650933549532729461435228973046000644775390625}{149123409304291820373991599415711301689966024432613919788367872}\cdot t^5+\frac{9273804343021570006821528794592635324332802350202721711688016403473959677151815380061176854517560293608851552734375}{1192987274434334562991932795325690413519728195460911358306942976}\cdot t^3-\frac{637340828080856025122679074713856554253453294550159625355909219706050612441713260540943337107766893259784755859375}{2385974548868669125983865590651380827039456390921822716613885952}\cdot t$

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.