Rule: Q[7, 38]

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.

• $P_1$:
  $\frac{429}{16}\cdot t^7-\frac{693}{16}\cdot t^5+\frac{315}{16}\cdot t^3-\frac{35}{16}\cdot t$
• $P_2$:
  $\frac{429}{16}\cdot t^{45}-\frac{72169911719419392897136001448880624089171490737}{240166388178154259150935929874091544426731728}\cdot t^{43}+\frac{94362391958628597289725166917705830704971198429}{60041597044538564787733982468522886106682932}\cdot t^{41}-\frac{9085730119350444824504858713689152554833785783975123}{1783475598610973528454850215245003808912909812128}\cdot t^{39}+\frac{1574405545923913016031961112535338866499758975936824333}{137327621093044961691023466573865293286294055533856}\cdot t^{37}-\frac{65280198100020112011591518437167581054392040641389291663}{3433190527326124042275586664346632332157351388346400}\cdot t^{35}+\frac{10142800656010243445540827898946996961875903039044784019}{421214972260179924514483742012275899575607817393760}\cdot t^{33}-\frac{2311404624307868512027434250287101011031153133197766687}{97098256592444073508208914554777885941130373490120}\cdot t^{31}+\frac{438472054521485818762569472908375617726301692161591917}{23543402577384782883767522956806083789942756222755}\cdot t^{29}-\frac{272532301615631574359877209264464821003356741479115537101}{23449228967075243752232452864978859454782985197863980}\cdot t^{27}+\frac{30397319280553686009730753910926624845721148667368820207663}{5236994469313471104665247806511945278234866694189622200}\cdot t^{25}-\frac{6799656284598375262234402848873620957808106058031620602185}{2932716902815543818612538771646689355811525348746188432}\cdot t^{23}+\frac{5737440046243483855578073478816303693952878984205994484853}{7778075263989050997189776742193393508891436794500760624}\cdot t^{21}-\frac{12156056069714101451910603238709430643733829962317557886947}{65558062939336286976313832541344316717799252982220696688}\cdot t^{19}+\frac{48673167774199221891526383559949495946420144477838125489}{1337919651823189530128853725333557484036719448616748912}\cdot t^{17}-\frac{9870184897932883884982674923345382040592622332132747970699}{1802846730831747891848630394886968709739479457011069158920}\cdot t^{15}+\frac{444870577360998283956072312863798163391454037642281044779}{721138692332699156739452157954787483895791782804427663568}\cdot t^{13}-\frac{36299347046964846747959246266551386844202641082267381215}{721138692332699156739452157954787483895791782804427663568}\cdot t^{11}+\frac{77451675766256781970149923075518886898284943412181795653}{27304933214233563525634711253469907912963388867094920170552}\cdot t^9-\frac{417986188201269677160832400074259129368840072258841255433}{4060691858904824283125735267605584514101003084652743053423584}\cdot t^7+\frac{418387505528953597491718019897965041519167018872009170051}{194333110390445162121017330663981544603405147622666988985271520}\cdot t^5-\frac{118124503877831653328866888398658314531209611605969507}{5552374582584147489171923733256615560097289932076199685293472}\cdot t^3+\frac{2441907106248548698879755231285442037862728600283939}{38866622078089032424203466132796308920681029524533397797054304}\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.