Rule: Q[2, 69]

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^{71}-\frac{170533302021161046858015404403489641244020743786}{35236959593376964507038384782516353459077539}\cdot t^{69}+\frac{97323173567289427238063346370812517899603918642183}{35236959593376964507038384782516353459077539}\cdot t^{67}-\frac{1040914220490846905432907238648761973305486381592647}{1051849540100804910657862232313920998778434}\cdot t^{65}+\frac{131465559126396314462125296738416212462992855555766530}{525924770050402455328931116156960499389217}\cdot t^{63}-\frac{24922676250728288346870059023971954847792015637826691935}{525924770050402455328931116156960499389217}\cdot t^{61}+\frac{7371889285241769826182549516454023137476265608611715071105}{1051849540100804910657862232313920998778434}\cdot t^{59}-\frac{1745797417039075061420115684764397525621325513141605807654555}{2103699080201609821315724464627841997556868}\cdot t^{57}+\frac{674188092475407813175146809750777710917170003475926698768677555}{8414796320806439285262897858511367990227472}\cdot t^{55}-\frac{107547497566117071679205131111292533503386135989378192246725964725}{16829592641612878570525795717022735980454944}\cdot t^{53}+\frac{14311075670608517506625621120968789420409524709640484433294254310175}{33659185283225757141051591434045471960909888}\cdot t^{51}-\frac{1599789579561161884837944395261079213469714622448130347101075465326125}{67318370566451514282103182868090943921819776}\cdot t^{49}+\frac{75498974022333216420806216232628933916387936978572295382263710326670875}{67318370566451514282103182868090943921819776}\cdot t^{47}-\frac{6037655968962248463369381755566126943765646608555252789296713492569455125}{134636741132903028564206365736181887843639552}\cdot t^{45}+\frac{409950646330370827284314735375137081014002952907219351655783544748559731875}{269273482265806057128412731472363775687279104}\cdot t^{43}-\frac{23655756358304355896468036005721502154475597917409498815320229449858421250625}{538546964531612114256825462944727551374558208}\cdot t^{41}+\frac{4639659180541679538036166613081249166541184704309900495497269348699977061686875}{4308375716252896914054603703557820410996465664}\cdot t^{39}-\frac{193091013879679170171565994772781557649318825302540153928572571776036619137868125}{8616751432505793828109207407115640821992931328}\cdot t^{37}+\frac{6806056453395598128323084787841799477869613011325351279829156562408635045598179375}{17233502865011587656218414814231281643985862656}\cdot t^{35}-\frac{202542553104190781125128711716260809842899239181144554434693217979833133365350878125}{34467005730023175312436829628462563287971725312}\cdot t^{33}+\frac{1266857296107712318750396154557024450473955731113494725070103223619128422313997359375}{17233502865011587656218414814231281643985862656}\cdot t^{31}-\frac{26503532852543378531659447975277538739662907851838926512148691046937216497797890440625}{34467005730023175312436829628462563287971725312}\cdot t^{29}+\frac{460537344738949528279155014838986893038428143317404124976568597717138876345865944409375}{68934011460046350624873659256925126575943450624}\cdot t^{27}-\frac{6592146836884960106147448134403977550298580828181484673118308412665331683894006858353125}{137868022920092701249747318513850253151886901248}\cdot t^{25}+\frac{153902333144931391800868699971846269410050478034716790322463705634662512893179748909296875}{551472091680370804998989274055401012607547604992}\cdot t^{23}-\frac{1447170073121516463194278109425962172633880725892752213827733373641240344932774382760828125}{1102944183360741609997978548110802025215095209984}\cdot t^{21}+\frac{10797622781208796949476563260720631567538101113675992577474928835174468171968447629904234375}{2205888366721483219995957096221604050430190419968}\cdot t^{19}-\frac{62741573283069752537662498012594806665621279538458965812468891388766994584910980399098453125}{4411776733442966439991914192443208100860380839936}\cdot t^{17}+\frac{138667062692508254483840231622471727789455421581212805254639281328232391815005305535665453125}{4411776733442966439991914192443208100860380839936}\cdot t^{15}-\frac{452447654422205053258707298189909901243179732749919062803264888785973057310303936576539296875}{8823553466885932879983828384886416201720761679872}\cdot t^{13}+\frac{1047344764545302364045678528762194186929316331276437890903993842286803244030944318086395078125}{17647106933771865759967656769772832403441523359744}\cdot t^{11}-\frac{1629287403793804433194499823312394989820970795392572323179756243714651924130013292227688359375}{35294213867543731519935313539545664806883046719488}\cdot t^9+\frac{12603442350548974307094194505517105864196455478942535494736355872929295737717096116460791640625}{564707421880699704318965016632730636910128747511808}\cdot t^7-\frac{6709371497152360091642294018959872521820837872314858233271303533362460827986228020009701484375}{1129414843761399408637930033265461273820257495023616}\cdot t^5+\frac{1587756055708799515146286280173728728093134888725377878845299107579386846301533252005023828125}{2258829687522798817275860066530922547640514990047232}\cdot t^3-\frac{103042933151280922975271916459365113341491076580278437215379757937244614962962977150196484375}{4517659375045597634551720133061845095281029980094464}\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.