Rule: Q[2, 3, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{37}-\frac{10492662711679377493332883892241}{742986232235014574457042747838}\cdot t^{35}+\frac{4568513647463626618743809293298375}{74670116339618964732932796157719}\cdot t^{33}-\frac{52317364023928890612265940449883900}{323570504138348847176042116683449}\cdot t^{31}+\frac{1979349753527534122219135178556257570}{6794980586905325790696884450352429}\cdot t^{29}-\frac{67279068445098721200167898713552181458}{177640206771953517099647122059213501}\cdot t^{27}+\frac{32871528226644855115733302098025846608}{89579249568762884691275044457210227}\cdot t^{25}-\frac{459095253195222532479443004723259276500}{1702005741806494809134225844686994313}\cdot t^{23}+\frac{11226768826289831097702526448065356775}{74000249643760643875401123682043231}\cdot t^{21}-\frac{256386526637355870964595777249086628775}{3922013231119314125396259555148291243}\cdot t^{19}+\frac{4431023407688104352957980584786814530}{206421749006279690810329450270962697}\cdot t^{17}-\frac{53688510256364986048464360317386961860}{10114665701307704849706143063277172153}\cdot t^{15}+\frac{65817153642380915216761099690745150250}{67912755423066018276598389139146727313}\cdot t^{13}-\frac{8613200017339300214022037892316803050}{67912755423066018276598389139146727313}\cdot t^{11}+\frac{99716850016846451283389006131127074600}{8760745449575516357681192198949927823377}\cdot t^9-\frac{1912963166908679418439266472483502340}{2920248483191838785893730732983309274459}\cdot t^7+\frac{67536175946218301480090953837283707845}{3112984883082500145762716961360207686573294}\cdot t^5-\frac{1057673481906213003642593190820399625}{3112984883082500145762716961360207686573294}\cdot t^3+\frac{17382621041307992443983348780154725}{10895447090788750510169509364760726903006529}\cdot t$

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.