Rule: Q[1, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{33}-\frac{12616216214138253508}{1539464155910747433}\cdot t^{31}+\frac{291121411424584524407954}{9536980445867080347435}\cdot t^{29}-\frac{279504537747669331539728}{4087277333943034434615}\cdot t^{27}+\frac{1477643651740203905909978}{14381160989799565603275}\cdot t^{25}-\frac{3332978961639791893293332}{30488061298375079078943}\cdot t^{23}+\frac{2160586129074733047787814}{25490018462575885787313}\cdot t^{21}-\frac{9270899287921135979071672}{190951541816138653178643}\cdot t^{19}+\frac{61640481883850929993031384}{2991574155119505566465407}\cdot t^{17}-\frac{356911902783568661036908972}{55432109344861426672741365}\cdot t^{15}+\frac{11037441609444188388210618}{7566922862949337609294853}\cdot t^{13}-\frac{651317328761057831615083744}{2792194536428305577829800757}\cdot t^{11}+\frac{211549946947466486089418974}{8376583609284916733489402271}\cdot t^9-\frac{1126844403817828682072812}{649755961307215763394356151}\cdot t^7+\frac{315909915645181613361782}{4653657560713842629716334595}\cdot t^5-\frac{128741214196416991586696}{103311197847847306379702628009}\cdot t^3+\frac{1641404673570471763603}{241059461644977048219306132021}\cdot t$

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.