Rule: Q[4, 5, 32]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^9-168\cdot t^7+432\cdot t^5-270\cdot t^3+45\cdot t$
• $P_3$:
  $16\cdot t^{41}-\frac{176199942834421206486699614771916870411115501667208}{32438330777928274825188044875952364404415805309}\cdot t^{39}+\frac{187584237899969020290619538177190256126223798751049392}{227068315445497923776316314131666550830910637163}\cdot t^{37}-\frac{2419539726752346854517213879557981175768775543991283462}{32438330777928274825188044875952364404415805309}\cdot t^{35}+\frac{1014372862444109274622251313680311153306611143187869747075}{227068315445497923776316314131666550830910637163}\cdot t^{33}-\frac{42659143001586785381769413705340387422776873951937089567110}{227068315445497923776316314131666550830910637163}\cdot t^{31}+\frac{44861816324516166699227814946221415114057252697755725639540}{7829941911913721509528148763160915545893470247}\cdot t^{29}-\frac{288756503062054798911596859032768692498904077467017604141855}{2237126260546777574150899646617404441683848642}\cdot t^{27}+\frac{19404942042660613332285524330923690962623229386820290549674665}{8948505042187110296603598586469617766735394568}\cdot t^{25}-\frac{487704896339348363593651605805782942444730950813187129649911875}{17897010084374220593207197172939235533470789136}\cdot t^{23}+\frac{2286601400774251674379777131827967383435377822647772145628525375}{8948505042187110296603598586469617766735394568}\cdot t^{21}-\frac{127052858490703835125592175650133547400442931499671734957683354625}{71588040337496882372828788691756942133883156544}\cdot t^{19}+\frac{1291008634798212817250066420350102292804910511533198634274114809125}{143176080674993764745657577383513884267766313088}\cdot t^{17}-\frac{4710914400448852139382301032101245170751927294852139151944183710125}{143176080674993764745657577383513884267766313088}\cdot t^{15}+\frac{6017867155496694368680164681595190722738502823877706120788389009375}{71588040337496882372828788691756942133883156544}\cdot t^{13}-\frac{83146451051907754408246601775756965724784846286138426973698692321875}{572704322699975058982630309534055537071065252352}\cdot t^{11}+\frac{739562384406692726410916872909189054645134825979516541520518266438125}{4581634581599800471861042476272444296568522018816}\cdot t^9-\frac{987702250282296244969953762004619160717977154435061917520298480968125}{9163269163199600943722084952544888593137044037632}\cdot t^7+\frac{178972962038164550502940748786592359286192124050123278289717294005625}{4581634581599800471861042476272444296568522018816}\cdot t^5-\frac{240680240368651875561966582235537585048972107162411138863287136484375}{36653076652798403774888339810179554372548176150528}\cdot t^3+\frac{26802627074204618133600274930228771410752733081173302735020759478125}{73306153305596807549776679620359108745096352301056}\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.