Rule: Q[3, 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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{53}-\frac{128008855888268914275007}{3880782021019994915088}\cdot t^{51}+\frac{26821482313068171794774975}{130652994707673162141296}\cdot t^{49}-\frac{863742036496053843999624775}{1077887206338303587665692}\cdot t^{47}+\frac{690204163857897312146673747275}{313665177044446344010716372}\cdot t^{45}-\frac{28637030384278693485080071925}{6336670243322148363852856}\cdot t^{43}+\frac{26891531813066337219571137389055}{3732298773316745386309332184}\cdot t^{41}-\frac{664882796382995320647031572501325}{72779826079676535033031977588}\cdot t^{39}+\frac{81841657947607006743205599787225}{8741436600662903667935014852}\cdot t^{37}-\frac{7949866012937507042679182297162725}{1014006645676896825480461722832}\cdot t^{35}+\frac{16431845727593357782060365372170425}{3042019937030690476441385168496}\cdot t^{33}-\frac{2939813241457809231726263258236205}{956392631717982233123617306762}\cdot t^{31}+\frac{13255083273702119805773775390356525}{9162858439362603975410140003494}\cdot t^{29}-\frac{84232760924669197935029454704535175}{149765341388202561529117460746764}\cdot t^{27}+\frac{10985967235208378394140496831918025}{61015509454452895437788595119052}\cdot t^{25}-\frac{479920039038613420451770733740125}{10169251575742149239631432519842}\cdot t^{23}+\frac{3050499924939652338779391028586435}{303690831148299638656265962069827}\cdot t^{21}-\frac{197417597001768647511338643416847575}{114997594728156129837839377637107824}\cdot t^{19}+\frac{26691018440079601245992891116353025}{114997594728156129837839377637107824}\cdot t^{17}-\frac{140659896314146947139671083053287475}{5778629135089845524351428726264668156}\cdot t^{15}+\frac{48310908561437506972404167987101075}{25040726252055997272189524480480228676}\cdot t^{13}-\frac{1289547031644179114174787943008205}{11557258270179691048702857452529336312}\cdot t^{11}+\frac{862166943681069720212295840890575}{192270751222080314719329355801169867736}\cdot t^9-\frac{808353915100190477248660776263575}{6932428752396118014046930661942180231148}\cdot t^7+\frac{4052766696395137196840046099025}{2310809584132039338015643553980726743716}\cdot t^5-\frac{217195691025430481192549627723495}{17386531311009463979229702100150988019719184}\cdot t^3+\frac{2302969785587148311136753817}{86500155776166487458854239304233771242384}\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.