Rule: Q[1, 6, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{21}{13}\cdot t^5+\frac{105}{143}\cdot t^3-\frac{35}{429}\cdot t$
• $P_3$:
  $t^{45}-\frac{2186967021800587663549575801481231033005196689}{195135190394750335560135443022699379846719529}\cdot t^{43}+\frac{125816522611504796386300222556941107606628264572}{2146487094342253691161489873249693178313914819}\cdot t^{41}-\frac{9085730119350444824504858713689152554833785783975123}{47819439487756727731695671396256664626477394337682}\cdot t^{39}+\frac{40369372972408026052101566988085611961532281434277547}{94412739501468411162578633269532389134327163179526}\cdot t^{37}-\frac{1673851233333849025938244062491476437292103606189469017}{2360318487536710279064465831738309728358179079488150}\cdot t^{35}+\frac{780215435077711034272371376842076689375069464541906463}{868755880286621094311122717900319042874691123374630}\cdot t^{33}-\frac{118533570477326590360381243604466718514418109394757266}{133510102814610601073787257512819593169054263548915}\cdot t^{31}+\frac{179885971085737771800028501706000253426175053194499248}{258977428351232611721442752524866921689370318450305}\cdot t^{29}-\frac{7623281164073610471604956902502512475618370391024210828}{17586921725306432814174339648734144591087238898397985}\cdot t^{27}+\frac{1558836886182240308191320713380852556190828136788144626034}{7200867395306022768914715733953924757572941704510730525}\cdot t^{25}-\frac{174350161143548083647035970483938998918156565590554374415}{2016242870685686375296120405507098932120423677263004547}\cdot t^{23}+\frac{13373986121779682647035136314257118167722328634512807657}{486129703999315687324361046387087094305714799656297539}\cdot t^{21}-\frac{311693745377284652613092390736139247275226409290193791973}{45071168270793697296215759872174217743486986425276728973}\cdot t^{19}+\frac{16224389258066407297175461186649831982140048159279375163}{11957656888169756425526630170168670013578180072012193401}\cdot t^{17}-\frac{6580123265288589256655116615563588027061748221421831980466}{32225885313617493566794268308604565686593195294072861215695}\cdot t^{15}+\frac{148290192453666094652024104287932721130484679214093681593}{6445177062723498713358853661720913137318639058814572243139}\cdot t^{13}-\frac{930752488383714019178442211962856072928272848263266185}{495782850978730670258373358593916395178356850678044018703}\cdot t^{11}+\frac{11915642425577966456946142011618290292043837448027968562}{112632849508713449543243183920563370140973979076766545703527}\cdot t^9-\frac{10717594569263325055405958976263054599201027493816442447}{2791725652997066694648942996478839353444439620698760849228714}\cdot t^7+\frac{975262250650241485994680699062855574636752957743611119}{12145819399402822632563583166498846537712821726416686811579470}\cdot t^5-\frac{3028833432764914187919663805093802936697682348871013}{3817257525526601398805697566613923197566886828302387283639262}\cdot t^3+\frac{62613002724321761509737313622703641996480220520101}{26720802678686209791639882966297462382968207798116710985474834}\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.