Rule: Q[1, 6, 30]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{21}{13}\cdot t^5+\frac{105}{143}\cdot t^3-\frac{35}{429}\cdot t$
• $P_3$:
  $t^{37}-\frac{19944450506125491474555725506986657}{2193874699098371736365588642099257}\cdot t^{35}+\frac{11907690248195282591317342971110813850}{313724081971067158300279175820193751}\cdot t^{33}-\frac{8253592974312346806657769053406349950}{85561113264836497718257957041871023}\cdot t^{31}+\frac{290118902286244654028453995297476088830}{1739742636385008786937911793184710801}\cdot t^{29}-\frac{21303915579818200477443734210877270454618}{102644815546715518429336795797897937259}\cdot t^{27}+\frac{28804127317654168865183082137012091112194}{150019345799045757704415316935389292917}\cdot t^{25}-\frac{20160235952416026830398832469559995318450}{150019345799045757704415316935389292917}\cdot t^{23}+\frac{570518084388431596220444054292602158504800}{7951025327349425158334011797575632524601}\cdot t^{21}-\frac{232623049149210078440061747710695803508800}{7951025327349425158334011797575632524601}\cdot t^{19}+\frac{3791054066250393023225946173788814712090}{418475017228917113596526936714506974979}\cdot t^{17}-\frac{41388205799759719587147698604326119971630}{19668325809759104339036766025581827824013}\cdot t^{15}+\frac{7068794392867000651202586946943034535450}{19668325809759104339036766025581827824013}\cdot t^{13}-\frac{728793365950827706863697507029524386950}{16642429531334626748415725098569238928011}\cdot t^{11}+\frac{883550098083304351148503992107059360185150}{242726808818237106648052729521705337176144433}\cdot t^9-\frac{11483784383176702021352922164718720510270}{59536764427114762008012933656267346854525993}\cdot t^7+\frac{2633132894124615010893821509692751616805}{450778359233868912346383640540309911898553947}\cdot t^5-\frac{37401668860355446843932502710127229325}{450778359233868912346383640540309911898553947}\cdot t^3+\frac{157724205505896542453249967182843100}{450778359233868912346383640540309911898553947}\cdot t$

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.