Rule: Q[2, 49]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{51}-\frac{1311924829953575}{68814769822942}\cdot t^{49}+\frac{380575186859220150}{3337516336412687}\cdot t^{47}-\frac{575681526358536850}{1349208731741299}\cdot t^{45}+\frac{4258608246497021025}{3802315516725479}\cdot t^{43}-\frac{108349810168869404415}{49430101717431227}\cdot t^{41}+\frac{768408531702235495050}{231541002781651537}\cdot t^{39}-\frac{23100669044846650950}{5803534209738889}\cdot t^{37}+\frac{67473751695280553452725}{17561494518669878114}\cdot t^{35}-\frac{258549085442468673552525}{85741414414682346086}\cdot t^{33}+\frac{747120726368171386195580}{385836364866070557387}\cdot t^{31}-\frac{334468546411409695441100}{327753471230318000361}\cdot t^{29}+\frac{164668381327734380396650}{372960846572430827997}\cdot t^{27}-\frac{498776890614658194070}{3187699543354109641}\cdot t^{25}+\frac{136745655061537239213300}{3025126866643050049309}\cdot t^{23}-\frac{206304356054738771644220}{19525818866514232136449}\cdot t^{21}+\frac{77202406907926255550525}{39051637733028464272898}\cdot t^{19}-\frac{763660460334642043702725}{2616459728112907106284166}\cdot t^{17}+\frac{567237514227663990522350}{17006988232733896190847079}\cdot t^{15}-\frac{146707138181941109129350}{51020964698201688572541237}\cdot t^{13}+\frac{14414124630397064180545}{79802021707443666741667063}\cdot t^{11}-\frac{111237778477571565664075}{14124957842217529013275070151}\cdot t^9+\frac{19858494649718529593950}{89458066334044350417408777623}\cdot t^7-\frac{3559397495740675821750}{984038729674487854591496553853}\cdot t^5+\frac{2910384321567147228475}{104308105345495712586698634708418}\cdot t^3-\frac{6009692764948206187}{93328304782811953367046146844374}\cdot t$

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.