Rule: Q[1, 8, 28]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-\frac{36}{17}\cdot t^7+\frac{126}{85}\cdot t^5-\frac{84}{221}\cdot t^3+\frac{63}{2431}\cdot t$
• $P_3$:
  $t^{37}-\frac{227410855942360222642876962072728438}{25343614258090607133097670536183407}\cdot t^{35}+\frac{5592219494344183841527481972850121529317}{151279015108220256401828595156424189725}\cdot t^{33}-\frac{8637931848618970945508438073379451004368}{93212322440418541823348932369109854275}\cdot t^{31}+\frac{5590082576420822022211958385988974523672563164}{35389456399341505681361772407918092823317875}\cdot t^{29}-\frac{390874658166061876180953045124283141754691176584}{2017199014762465823837621027251331290929118875}\cdot t^{27}+\frac{55823185771272085406432259534229927358262230092}{316085315703520285786521813386960743592881875}\cdot t^{25}-\frac{3546715747876137394661779357605391025785198736}{29134820403976652429018532364363338105083025}\cdot t^{23}+\frac{8643945306457490102218663396247085408099768862}{135079621872982661261813195507502749396294025}\cdot t^{21}-\frac{1156341987047304440434591042953156720075809012}{45026540624327553753937731835834249798764675}\cdot t^{19}+\frac{6183029701686756568707526085729679027458298}{789939309198729013226977751505864031557275}\cdot t^{17}-\frac{1248038271935292389337056816319093534909904}{697005272822407952847333310152232969021125}\cdot t^{15}+\frac{1807987263353145141191081190407376198523628}{5994245346272708394487066467309203533581675}\cdot t^{13}-\frac{187459632201140950356737119821286872847016}{5155889353787014912740623604748475766647175}\cdot t^{11}+\frac{198954198461304378724286042307500575512078292}{66155216298441188345374941472527692561849902425}\cdot t^9-\frac{12955481190851721478395873457820900420048464}{80856375475872563533236039577533846464483214075}\cdot t^7+\frac{286796757964707358115104259978599282833913}{57754553911337545380882885412524176046059438625}\cdot t^5-\frac{368131457075251637202598936294772200518266}{4955340725592761393679751568394574304751899834025}\cdot t^3+\frac{9683742760613877026474740465158122784323}{28080264111692314564185258887569254393594099059475}\cdot t$

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.