Rule: Q[4, 10, 16]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{14}-\frac{436215}{27784}\cdot t^{12}+\frac{12954799}{583464}\cdot t^{10}-\frac{3039465}{194488}\cdot t^8+\frac{2679105}{472328}\cdot t^6-\frac{8846695}{8974232}\cdot t^4+\frac{1485}{22952}\cdot t^2-\frac{273}{390184}$
• $P_3$:
  $\frac{35}{8}\cdot t^{30}-\frac{5084437683310812421076751162992773531579271695875440998815}{151407372723241211980170210716064486265213936895896088584}\cdot t^{28}+\frac{163680520385314674565120821379193654505613895954934949539068989}{1412782194880563748986968236191597721340711245175606402577304}\cdot t^{26}-\frac{1005348884478160786092705444722170629836365243769215994442959275}{4238346584641691246960904708574793164022133735526819207731912}\cdot t^{24}+\frac{154615561544374540318389326825179692649354056293892745960525}{482472039714399796425149358478170362653936838360749211736}\cdot t^{22}-\frac{237633109576663563473827688901761274719888787913730255732812296125}{790780702211501635822724326340858458720875001748385852056266488}\cdot t^{20}+\frac{102805059038957841742214836907708915411719056740458224918110055625}{513313789154834395183171931133539701274953948503338184668102808}\cdot t^{18}-\frac{25958658366425887954850962056758439479843055501989907100450826525}{271754358964324091567561610600109253616152090384120215412525016}\cdot t^{16}+\frac{3729233863497761898002720402747923239043297968090755156745547540375}{115133263414551973460790269024246287115376435626072264596439765112}\cdot t^{14}-\frac{6168279222917290949481024387624882296634380647983787204253596775125}{805932843901863814225531883169724009807635049382505852175078355784}\cdot t^{12}+\frac{26436404203723927826625010678329848527222777840294622084202101446375}{21760186785350322984089360845582548264806146333327658008727115606168}\cdot t^{10}-\frac{294712357976657604094950855221607758852797264773147136166405230115}{2417798531705591442676595649509172029422905148147517556525235067352}\cdot t^8+\frac{55399287274899045156031604066104469419803700576442546428202717503}{7944195175604086168794528562672993810960974058198986257154343792728}\cdot t^6-\frac{4476687023433465560473913430049297511985260203295535313490619985}{23832585526812258506383585688018981432882922174596958771463031378184}\cdot t^4+\frac{1106501334873073678198612299403154665060892842967675916433855}{729177334958829165251671703820226485064050758965124342444118512376}\cdot t^2-\frac{112856074158591726759884390135553573167779232916878711435}{111564132248700862283505770684494652214799766121664024393950132393528}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.