Rule: Q[1, 18, 20]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{19}-\frac{171}{37}\cdot t^{17}+\frac{11628}{1295}\cdot t^{15}-\frac{3876}{407}\cdot t^{13}+\frac{75582}{12617}\cdot t^{11}-\frac{75582}{33263}\cdot t^9+\frac{16796}{33263}\cdot t^7-\frac{50388}{831575}\cdot t^5+\frac{12597}{3825245}\cdot t^3-\frac{4199}{80330145}\cdot t$
• $P_3$:
  $t^{39}-\frac{14781}{1517}\cdot t^{37}+\frac{110853327}{2529905}\cdot t^{35}-\frac{11796566093}{97798899}\cdot t^{33}+\frac{1730387842513252}{7612580353673}\cdot t^{31}-\frac{90709297733300428}{291979291629587}\cdot t^{29}+\frac{864455535368955432604}{2715800073961143717}\cdot t^{27}-\frac{28598377181097561437028468}{114750097013952658553575}\cdot t^{25}+\frac{1317751195800797323139666235702}{8747643165579280741175155829}\cdot t^{23}-\frac{3949536596798674474668812998245478}{55996706561365351426259102950413}\cdot t^{21}+\frac{7078432311717584834357735360763643106}{277362353637787607585961576742529001}\cdot t^{19}-\frac{34450244058808202119683936995639794}{4866006204171712413788799591974193}\cdot t^{17}+\frac{235892972556644361184651555070883772}{158860790783252964097222574914451595}\cdot t^{15}-\frac{2441075087659680694111346551221956}{10590719385550197606481504994296773}\cdot t^{13}+\frac{2990096828362790833089012743071172}{116497913241052173671296554937264503}\cdot t^{11}-\frac{1929837664080407985935549240228636}{984936902856168377402779964469599889}\cdot t^9+\frac{2127721989736757259628890392309531}{22215799031089131179196036976369864163}\cdot t^7-\frac{383765915316134443936486543434521}{142815850914144414723403094848091983905}\cdot t^5+\frac{9131678489441746988055623894707}{257068531645459946502125570726565571029}\cdot t^3-\frac{276219708581357823053539811719}{1970858742615192923182962708903669377889}\cdot t$

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.