Rule: Q[16, 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.

• $P_1$:
  $t^{16}-120\cdot t^{14}+5460\cdot t^{12}-120120\cdot t^{10}+1351350\cdot t^8-7567560\cdot t^6+18918900\cdot t^4-16216200\cdot t^2+2027025$
• $P_2$:
  $t^{48}-\frac{2116440634113003393240360}{2470287875140857532409}\cdot t^{46}+\frac{395702225068397718947581740}{1181442027241279689413}\cdot t^{44}-\frac{2156106274616296379560706262840}{27173166626549432856499}\cdot t^{42}+\frac{346739347682244462271658480625750}{27173166626549432856499}\cdot t^{40}-\frac{763501350353707230082071823909445560}{516290165904439224273481}\cdot t^{38}+\frac{198212531387823968895080500034374065700}{1548870497713317672820443}\cdot t^{36}-\frac{6746333543594432141116229305759714229800}{797902983670496982968107}\cdot t^{34}+\frac{345076723797731307411961447069608117060725}{797902983670496982968107}\cdot t^{32}-\frac{13776653504453356916346527642624943023006000}{797902983670496982968107}\cdot t^{30}+\frac{430890988807488466784615482964814267391641000}{797902983670496982968107}\cdot t^{28}-\frac{10558395471284817214196668415730246738274302000}{797902983670496982968107}\cdot t^{26}+\frac{202014983841296829733645666176091389698614612500}{797902983670496982968107}\cdot t^{24}-\frac{130345151179775014821922608637936228129865550000}{34691434072630303607309}\cdot t^{22}+\frac{78158846553381659225245504325562259273849725000}{1825864951191068610911}\cdot t^{20}-\frac{673855182233885483850193605057081493350011610000}{1825864951191068610911}\cdot t^{18}+\frac{253633513829700057253880103242555977660940690625}{107403820658298153583}\cdot t^{16}-\frac{1173419507824716494695258571141334854591361675000}{107403820658298153583}\cdot t^{14}+\frac{344415317151434071222768755226072356952873537500}{9763983696208923053}\cdot t^{12}-\frac{738680669315109472231282302736757913413264625000}{9763983696208923053}\cdot t^{10}+\frac{979456368925920286125761642038125559405185806250}{9763983696208923053}\cdot t^8-\frac{717851571470255821970233512748347841164265875000}{9763983696208923053}\cdot t^6+\frac{239769423992813954693711475111792199422900187500}{9763983696208923053}\cdot t^4-\frac{24848406021844423924462932215797429367587875000}{9763983696208923053}\cdot t^2+\frac{315906529272927452123758867790612666173828125}{9763983696208923053}$

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.