Rule: Q[5, 62]

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^{67}-\frac{593301481884155685435151320699328813063551345935427668912}{17611964765029972453417171637800543410212110687536561}\cdot t^{65}+\frac{8509207350115261857407769667848857932439349723180808040484560}{510746978185869201149097977496215758896151209938560269}\cdot t^{63}-\frac{876909939933976872273136011907863585438236045658683672872460280}{170248992728623067049699325832071919632050403312853423}\cdot t^{61}+\frac{3224719169751258980678158392023995825201607786419886995574088300}{2885576147942763848299988573424947790373735649370397}\cdot t^{59}-\frac{18018905494154818824479441051644212390063197739881899526768923830}{99502625791129787872413399083618889323232263771393}\cdot t^{57}+\frac{2266120773162966831334826483170538647275764397612659674155190685505}{99502625791129787872413399083618889323232263771393}\cdot t^{55}-\frac{453827913905719563883624291398329287501178814724821122645280203996025}{199005251582259575744826798167237778646464527542786}\cdot t^{53}+\frac{73664978256866972065107790273657577198405085313155681893976435351204825}{398010503164519151489653596334475557292929055085572}\cdot t^{51}-\frac{9815666166226296460575317928501756363236140592528260609461240650445395625}{796021006329038302979307192668951114585858110171144}\cdot t^{49}+\frac{1083534567282960974160263181959428517976244564026047665295304384828251425125}{1592042012658076605958614385337902229171716220342288}\cdot t^{47}-\frac{99736520788445897994897157560147567077992056850164124053871571827395005557125}{3184084025316153211917228770675804458343432440684576}\cdot t^{45}+\frac{7689187763259674009687897529314894313802418020713406216194117335537077483276875}{6368168050632306423834457541351608916686864881369152}\cdot t^{43}-\frac{497867723207184410855221138085264369198788491037915291587894531248568719560749375}{12736336101264612847668915082703217833373729762738304}\cdot t^{41}+\frac{27109348734695200010587076914690391024532227856044880365100454003995545063047003125}{25472672202529225695337830165406435666747459525476608}\cdot t^{39}-\frac{1241359732158007418757676849660048667204201419412614657184778015476548036808911108125}{50945344405058451390675660330812871333494919050953216}\cdot t^{37}+\frac{23872320639642513964373331408207781968138595144519640895001181053553184908913763333125}{50945344405058451390675660330812871333494919050953216}\cdot t^{35}-\frac{384679779348018697993144042518652110087173097710742418734542592337822236838009340071875}{50945344405058451390675660330812871333494919050953216}\cdot t^{33}+\frac{41403295344077142713656301662227785619922731962538430856143205704416088681099321778971875}{407562755240467611125405282646502970667959352407625728}\cdot t^{31}-\frac{925605393054451891116651619363767041258023636759691845915629900723067417658897175219421875}{815125510480935222250810565293005941335918704815251456}\cdot t^{29}+\frac{17084094471314952135435377422542935611942494657830865260119150384030073729873637179647603125}{1630251020961870444501621130586011882671837409630502912}\cdot t^{27}-\frac{258281274756099809977840731666079738719081728046359880820845567437270389774332031202681690625}{3260502041923740889003242261172023765343674819261005824}\cdot t^{25}+\frac{3167133076928915253093500943167507557793829747551041352279508523237947525500596141682446171875}{6521004083847481778006484522344047530687349638522011648}\cdot t^{23}-\frac{31121083322920347430184469555595941267836858511884087586570574382898849222967734706144739296875}{13042008167694963556012969044688095061374699277044023296}\cdot t^{21}+\frac{241412934380815841307509888806505308036543964392441452254129298727554830693416691079012793359375}{26084016335389927112025938089376190122749398554088046592}\cdot t^{19}-\frac{1451084964060144039414587755536566266943342017824338748359201015713639501258371204329693016234375}{52168032670779854224051876178752380245498797108176093184}\cdot t^{17}+\frac{6601535804482724745007204452444510277416325557937989192906159427432560482151992178947226458484375}{104336065341559708448103752357504760490997594216352186368}\cdot t^{15}-\frac{22054351889757846831862328930893458062276315251769311748441316633296321529717674553524966201484375}{208672130683119416896207504715009520981995188432704372736}\cdot t^{13}+\frac{51989603682124470829894338936520832535972768314466652297164117553333947899722807388784961893515625}{417344261366238833792415009430019041963990376865408745472}\cdot t^{11}-\frac{81881875034915875620583579837122357368136753342566105638886992373003774942309484586727960201953125}{834688522732477667584830018860038083927980753730817490944}\cdot t^9+\frac{79633667262119971457614501049315396039042858068589330725483357656761934717096588401534323312734375}{1669377045464955335169660037720076167855961507461634981888}\cdot t^7-\frac{42303090060921177655981987484104611973622403277999507582460199431870334075230215842621563882109375}{3338754090929910670339320075440152335711923014923269963776}\cdot t^5+\frac{19771967520806277939824949230047225176698178039626859507324581100557143354143629347836444948046875}{13355016363719642681357280301760609342847692059693079855104}\cdot t^3-\frac{1246679625980249332935359478454768162693741581530239066635354896244432718400275531573457398828125}{26710032727439285362714560603521218685695384119386159710208}\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.