Rule: Q[6, 7, 14]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{13}-\frac{3731}{80}\cdot t^{11}+\frac{1182181}{20400}\cdot t^9-\frac{200960617}{5814000}\cdot t^7+\frac{1942171}{193800}\cdot t^5-\frac{241297}{193800}\cdot t^3+\frac{38549}{872100}\cdot t$
• $P_3$:
  $\frac{231}{16}\cdot t^{27}-\frac{43628325515666031917851426168046714182678005153547306322891}{434112750329433056103197949260124924351452023814902484720}\cdot t^{25}+\frac{3447417271563978540592359268215938524660812362488452941599327}{11069875133400542930631547706133185570962026607280013360360}\cdot t^{23}-\frac{958253792860215742976024943685787482592418453648227998750270401361}{1692611582584776515450890223137029406764021273319632242832444900}\cdot t^{21}+\frac{9447754550846660836300442762908007346499107726677503167279314399573}{14105096521539804295424085192808578389700177277663602023603707500}\cdot t^{19}-\frac{8160125049308390661724515652202451976369502606549497934423574613}{15088892299464916875721100976474730840500831490868209267868750}\cdot t^{17}+\frac{2468002351586438514135842323895702753741829841501621398164287046201}{8122439482991961606652878779759738639270071125837244508948265000}\cdot t^{15}-\frac{9336788635391968047610986731056428438037959274902265455583341146341}{78516915002255628864311161537677473512944020883093363586499895000}\cdot t^{13}+\frac{45124159310784289277944144114818259250341387724293843591286703807863}{1413304470040601319557600907678194523232992375895680544556998110000}\cdot t^{11}-\frac{24119809607145744620329779665842439469140390944149249785163771674291}{4239913410121803958672802723034583569698977127687041633670994330000}\cdot t^9+\frac{466953088875027465867106720494295577140276253240105208580550013526}{736096078146146520602917139415726314183850195779000283623436515625}\cdot t^7-\frac{47124963542829584547632662839938059225442863912655017404588867259}{1177753725033834432964667423065162102694160313246400453797498425000}\cdot t^5+\frac{319533677880950081539086426113184006983537463838094213666207377}{270693396479550655963653399656105805861157813931632362364747621875}\cdot t^3-\frac{988003937446431273574274589763242565732773100562083710771776741}{95103613296482130461896894412511839792553445294646836644147997818750}\cdot t$

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.