Rule: Q[4, 54]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{58}-\frac{240905980609553820990869050871162091004100960073}{156076154376443784020471091257586920927888413}\cdot t^{56}+\frac{4319816504751694665659618738495126129086684077976896}{3901903859411094600511777281439673023197210325}\cdot t^{54}-\frac{1914444930812134195092409917939403975608567681279095676}{3901903859411094600511777281439673023197210325}\cdot t^{52}+\frac{34587858134481660284478592287171583651388751293211735489}{229523756435946741206575134202333707246894725}\cdot t^{50}-\frac{313103327864853580056994855510085933893495397465880034137}{9180950257437869648263005368093348289875789}\cdot t^{48}+\frac{54196147575171769228021015857859068308869387394694249390984}{9180950257437869648263005368093348289875789}\cdot t^{46}-\frac{7351876411998805845777536179732248881077890309256800035439888}{9180950257437869648263005368093348289875789}\cdot t^{44}+\frac{794538845014129648470699268513392214962153278336572792544979633}{9180950257437869648263005368093348289875789}\cdot t^{42}-\frac{69177487823800388923668858675473939865661041605149032198053267109}{9180950257437869648263005368093348289875789}\cdot t^{40}+\frac{4888145302517108997879390145696515170480750914679834100904051972440}{9180950257437869648263005368093348289875789}\cdot t^{38}-\frac{281567644604460219085343169128993648410944110025603715206895053907980}{9180950257437869648263005368093348289875789}\cdot t^{36}+\frac{779333637989924765643210269685418935211618979283419582967216903376845}{540055897496345273427235609887844017051517}\cdot t^{34}-\frac{29953719089485537915319425979961383177602128725119829198718300016537845}{540055897496345273427235609887844017051517}\cdot t^{32}+\frac{30276261629021532104201474272871681040640786704618603710956776541302960}{17421157983753073336362439028640129582307}\cdot t^{30}-\frac{770414776340252864935692401887155484213974516783262599472426766331475200}{17421157983753073336362439028640129582307}\cdot t^{28}+\frac{15827838074432466441339204342458276552820853695777100397796891393111866025}{17421157983753073336362439028640129582307}\cdot t^{26}-\frac{260447175123455310528954174062809760942587897966400013532752871124826895125}{17421157983753073336362439028640129582307}\cdot t^{24}+\frac{57745406370785074640581295287043172693298460786896644549687362626254724554000}{296159685723802246718161463486882202899219}\cdot t^{22}-\frac{588951779246619803436795936930930678633926104882460660593352088497066773759500}{296159685723802246718161463486882202899219}\cdot t^{20}+\frac{16670128167846588697048695682599561283528776789042767862362650047380160020625}{1069168540519141684903109976486939360647}\cdot t^{18}-\frac{1601719386333225827265394935155227513552067890041845876657879164516684547563125}{17421157983753073336362439028640129582307}\cdot t^{16}+\frac{6905924648637554141906165847327737022719282450606705420147462656284186716535000}{17421157983753073336362439028640129582307}\cdot t^{14}-\frac{20978544851996592486917274977193483162058560076712419723608664623513802145610000}{17421157983753073336362439028640129582307}\cdot t^{12}+\frac{42713170349850561155381000153393496356203614985665963913784416637898486396283125}{17421157983753073336362439028640129582307}\cdot t^{10}-\frac{54370761792643034557102493761731183274925589864972879043430856425611512784715625}{17421157983753073336362439028640129582307}\cdot t^8+\frac{39097651929666837491912944793513058165272284209898825752928810035389573391525000}{17421157983753073336362439028640129582307}\cdot t^6-\frac{13573005247103989397517150120504943550216897756238272443055338494852636004177500}{17421157983753073336362439028640129582307}\cdot t^4+\frac{1732666741636409132971923115171010390371477989116234686321365942463579342580625}{17421157983753073336362439028640129582307}\cdot t^2-\frac{38861352563804617800545142221247228372176854072008492018589507033117973735625}{17421157983753073336362439028640129582307}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.