Rule: Q[2, 50]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{52}-\frac{801305824157007}{42033367295824}\cdot t^{50}+\frac{14381604551034175}{126100101887472}\cdot t^{48}-\frac{4787587978752927075}{11212400726161052}\cdot t^{46}+\frac{238997866226406889875}{213035613797059988}\cdot t^{44}-\frac{2640063025533611081495}{1200746186856156296}\cdot t^{42}+\frac{4004780945583898058565}{1200746186856156296}\cdot t^{40}-\frac{214298625264609952937325}{53433205315098955172}\cdot t^{38}+\frac{10218452158658277003925}{2630836934020152292}\cdot t^{36}-\frac{190756755584459308846875}{62312407381061584624}\cdot t^{34}+\frac{53511049503789860716568835}{27076573724935407389264}\cdot t^{32}-\frac{3090717569237819540897605}{2947852784569580643186}\cdot t^{30}+\frac{136034316164585252898575}{297420651316726527218}\cdot t^{28}-\frac{97411359757771447004225}{594841302633453054436}\cdot t^{26}+\frac{940567338924816180725875}{19629762986903950796388}\cdot t^{24}-\frac{2717518133564488868481595}{238828783007331401356054}\cdot t^{22}+\frac{1673850780717199076171270}{770765617887296795285447}\cdot t^{20}-\frac{12162567954729961868287825}{36996749658590246173701456}\cdot t^{18}+\frac{439013476992112863752275}{11318640306509344719808208}\cdot t^{16}-\frac{719887249452151890227125}{206565185593795541136499796}\cdot t^{14}+\frac{429832627123204209075535}{1859086670344159870228498164}\cdot t^{12}-\frac{273595172262070259335735}{25200952642443056018652975112}\cdot t^{10}+\frac{505206367259735957044775}{1486856205904140305100525531608}\cdot t^8-\frac{274391627879235348138475}{42375401868267998695364977650828}\cdot t^6+\frac{913887638473076847125}{14125133956089332898454992550276}\cdot t^4-\frac{8325641809381969085741}{32939812385600324319197042627243632}\cdot t^2+\frac{269255006018778717917}{1679930431665616540279049173989425232}$

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.