Rule: Q[2, 12, 23]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{14}-\frac{248498}{1555}\cdot t^{12}+\frac{3530769}{1555}\cdot t^{10}-\frac{8883963}{622}\cdot t^8+\frac{50229333}{1244}\cdot t^6-\frac{114812775}{2488}\cdot t^4+\frac{78937551}{4976}\cdot t^2-\frac{6151761}{9952}$
• $P_3$:
  $4\cdot t^{37}-\frac{5206884703785885069401677643109785203839199881736405351984973}{5533163732601681780572327747967800058999238948871169643830}\cdot t^{35}+\frac{2156429944282243047560762390617286453826152091146369834371071307}{22132654930406727122289310991871200235996955795484678575320}\cdot t^{33}-\frac{86671141549637352704475679652555623951611997891451497886174682427}{14755103286937818081526207327914133490664637196989785716880}\cdot t^{31}+\frac{123518601412956111184936671657539022617506177131307392658484794715885}{537085759644536578167553946736074459060192793970428200094432}\cdot t^{29}-\frac{6634894636616140976129239001203571630003689171698638172481741732529783}{1074171519289073156335107893472148918120385587940856400188864}\cdot t^{27}+\frac{27984193286268544860406840523333155528054351995643712525407140010370871}{238704782064238479185579531882699759582307908431301422264192}\cdot t^{25}-\frac{762319826189697387389954799944129656121308992952344429367894845400093273}{477409564128476958371159063765399519164615816862602844528384}\cdot t^{23}+\frac{2141154568056680646228102431828154896676041637403169249211150215822469967}{136402732608136273820331161075828434047033090532172241293824}\cdot t^{21}-\frac{2332727986225237200396896324418045137505390260409204757726171557292053045}{20985035785867119049281717088588989853389706235718806352896}\cdot t^{19}+\frac{306647904980060519990721883441138932051996577804641660311663146649331107295}{545610930432545095281324644303313736188132362128688965175296}\cdot t^{17}-\frac{2177945703339572817190900580135097263659178954192712199266029099102007723105}{1091221860865090190562649288606627472376264724257377930350592}\cdot t^{15}+\frac{10594131628712078808649316189348036060554190415129309632821986435893666840505}{2182443721730180381125298577213254944752529448514755860701184}\cdot t^{13}-\frac{2615777001630548106955338323855385492351061247026664881831433485591159869255}{335760572573873904788507473417423837654235299771500901646336}\cdot t^{11}+\frac{5243227607723868206507210155028908789967102821968911098249588328935428433575}{671521145147747809577014946834847675308470599543001803292672}\cdot t^9-\frac{6025327761610584106536736008289786718370542873480159816510125947967967444025}{1343042290295495619154029893669695350616941199086003606585344}\cdot t^7+\frac{3440106866321040850522941439207881228368189838811425201201348807406843590225}{2686084580590991238308059787339390701233882398172007213170688}\cdot t^5-\frac{754916267618211034491302104174238743065302564319660875949733949124139476225}{5372169161181982476616119574678781402467764796344014426341376}\cdot t^3+\frac{10968860114584057416273968979414201488964692856321689645227909669688919075}{2686084580590991238308059787339390701233882398172007213170688}\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.