Rule: Q[4, 49]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{53}-\frac{35494244910246934992855244729935917895}{635698590754030411481792344727264116}\cdot t^{51}+\frac{4694277545306993455175886096827148251121}{13985368996588669052599431583999810552}\cdot t^{49}-\frac{642882789092401053619026609980860838518111}{508717797250912836788304323867993108829}\cdot t^{47}+\frac{492790563903112965131299176121194815223637}{147454433985771836750233137353041480820}\cdot t^{45}-\frac{5210695345185957251795920830480340487836653}{789551469251087380417157435463103929118}\cdot t^{43}+\frac{15948855354170697294799674960184521430159087}{1579102938502174760834314870926207858236}\cdot t^{41}-\frac{431156886926811102496589675299094866043078217}{35135040381673388428563505878108124845751}\cdot t^{39}+\frac{177965571636644922582397153550058379290239157}{14793701213336163548868844580256052566632}\cdot t^{37}-\frac{355728598388525847865785192754651681908624349}{36984253033340408872172111450640131416580}\cdot t^{35}+\frac{224893038342092208902267295275499163244014663431}{35608438820500145662127308904676318527883224}\cdot t^{33}-\frac{45654969092347335293152015504802981009298594422}{13353164557687554623297740839253619447956209}\cdot t^{31}+\frac{935934231640864699738576317638016723734097800419}{612522580678442021752560886239311188870765458}\cdot t^{29}-\frac{21809165971784872088187291864547301776787476793}{38722691881970472639529711199036914238956437}\cdot t^{27}+\frac{36719358493050046628481168766478629018621893239}{215126066010947070219609506661316190216424650}\cdot t^{25}-\frac{39861794171667863029427245815664916801322416554}{942252169127948167561889639176564913147939967}\cdot t^{23}+\frac{137996075071909117204458919831302697937067251133}{16218158547414380581065251971281480929334239432}\cdot t^{21}-\frac{11143305488069565074959560902518448958715891349}{8109079273707190290532625985640740464667119716}\cdot t^{19}+\frac{7847427035009393074509667122875549869091156993}{44655477644250554750604323920925721462961398984}\cdot t^{17}-\frac{11865103040043350227261199884109213536123489801}{679135389172977186832107426297412013915871276215}\cdot t^{15}+\frac{715970870410778740120375272914933564477898251}{543308311338381749465685941037929611132697020972}\cdot t^{13}-\frac{10882077543274746375306410575131181059030263429}{149138131462385790228330790814911678255925332256814}\cdot t^{11}+\frac{16610870620696301874242919138253568259442015799}{5866099837520507748981011105386526011399729735434684}\cdot t^9-\frac{35165050261558702369025861390044341763783351}{488841653126708979081750925448877167616644144619557}\cdot t^7+\frac{302516863661721739980071454348927309819931661059}{281983419189610807493517203835930305367985008382345259880}\cdot t^5-\frac{72515691891525767139035138370011594920593177}{9399447306320360249783906794531010178932833612744841996}\cdot t^3+\frac{4487749874989087841218596920191693661423}{264773163558320007036166388578338314899516439795629352}\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.