Rule: Q[6, 33]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{39}-\frac{150613711350408922874726569775037}{1075249368990431120355066348400}\cdot t^{37}+\frac{5530081953701444240315045097159907}{8817044825721535186911544056880}\cdot t^{35}-\frac{3046583785412674557784528114835901919}{1772226009970028572569220355432880}\cdot t^{33}+\frac{476333612665992725575217034096739567}{147685500830835714380768362952740}\cdot t^{31}-\frac{313052058558355566368043938639232083161}{71332096901293650045911119306173420}\cdot t^{29}+\frac{1439252044091724777816650359140147740111}{321521520515683200945855537759353100}\cdot t^{27}-\frac{294157233292133870971857640837418952561}{84310087601890261581357674345785924}\cdot t^{25}+\frac{353974788161888382240061175566613043417}{168620175203780523162715348691571848}\cdot t^{23}-\frac{1115307311579986215185268164797549}{1139995640706229494112859239496}\cdot t^{21}+\frac{136905234564858432398055468529875146949}{388559534165233379461909281767535128}\cdot t^{19}-\frac{189000428080519232577942402667279727397}{1942797670826166897309546408837675640}\cdot t^{17}+\frac{193311281769966367547039828558323155361}{9519708587048217796816777403304610636}\cdot t^{15}-\frac{200498414412308054779631011653860599797}{63918043370180890921484076850759528556}\cdot t^{13}+\frac{376568382784022836557848955277410793}{1083356667291201541042102997470500484}\cdot t^{11}-\frac{217711772672660379780820169335392503287}{8245427594753334928871445913747979183724}\cdot t^9+\frac{2894308772201385573317733675782120413707}{2253750209232578213891528549757780976884560}\cdot t^7-\frac{16159244666218687553331284890150825971}{450750041846515642778305709951556195376912}\cdot t^5+\frac{212528162596014950023634298032466217}{450750041846515642778305709951556195376912}\cdot t^3-\frac{5838995399459618470155391738657779}{3155250292925609499448139969660893367638384}\cdot t$

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.