Rule: Q[1, 2, 42]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{45}-\frac{1364494424873097033}{124522573335021140}\cdot t^{43}+\frac{592371541037941974099}{10584418733476796900}\cdot t^{41}-\frac{15543751879381937433159}{87850675487857414270}\cdot t^{39}+\frac{34067737941548007816483}{87850675487857414270}\cdot t^{37}-\frac{8681000880212010151179469}{13880406727081471454660}\cdot t^{35}+\frac{20715890931989077550119667}{26944318940805209294340}\cdot t^{33}-\frac{3757958031132977089960126}{5103090708485835093625}\cdot t^{31}+\frac{41501622874437331337736524}{74505124343893192366925}\cdot t^{29}-\frac{1100875541834706512131224331}{3283363755568810339480350}\cdot t^{27}+\frac{1351617336140718070847573787}{8390818486453626423116450}\cdot t^{25}-\frac{3469354003353593661612425301}{56218483859239297034880215}\cdot t^{23}+\frac{229341461471522554038757327}{12221409534617238485843525}\cdot t^{21}-\frac{21953742236834652585375153}{4888563813846895394337410}\cdot t^{19}+\frac{248991674557471005899677251}{298202392644660619054582010}\cdot t^{17}-\frac{1041914445845292642715443842}{8796970583017488262110169295}\cdot t^{15}+\frac{109958329537450938774119337}{8796970583017488262110169295}\cdot t^{13}-\frac{1834549057915189168584112809}{1935333528263847417664237244900}\cdot t^{11}+\frac{275173226994428812101319631}{5594873290799122534702067671620}\cdot t^9-\frac{25746134491543097835644259}{15852140990597513848322525069590}\cdot t^7+\frac{482714274462158000246439}{15852140990597513848322525069590}\cdot t^5-\frac{2758171113084521264860483}{10430708771813164112196221495790220}\cdot t^3+\frac{34821925198302866587041}{52153543859065820560981107478951100}\cdot t$

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.