Rule: Q[1, 6, 46]

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^{53}-\frac{497358798350424908828226205924038373588938096455279}{37328816368371875061089885084028121119367704491703}\cdot t^{51}+\frac{16779213139123763271764079492030611845404086060538694}{200346427391383194491166630201322318072503860679491}\cdot t^{49}-\frac{2815030228865141493149650489035518578910875365924668438026}{8524024962548385699904528805672688482849066043838486725}\cdot t^{47}+\frac{9442622520003800536051444880156400667751891903815445118801248}{10305546179720998311184575326058280375764520847000730450525}\cdot t^{45}-\frac{514699059097775260230717853385490941506787335503102444581984}{270650707750248440495756523714661908858462163658605042135}\cdot t^{43}+\frac{1800469196394572867531268638706687361351900659265629856650234}{587510072921271004978593429526949021668369086966240213415}\cdot t^{41}-\frac{40158131398931249662863232357133647705407761650990551523870910}{10222675268830115486627525673768912977029622113212579713421}\cdot t^{39}+\frac{1404070953451299249500005528294347564909799894488314276214337}{344894577220989051505652013285051045108961609757509437025}\cdot t^{37}-\frac{98702116702740717749590710423389503891950874704044670317216587}{28626249909342091274969117102659236744043813609873283273075}\cdot t^{35}+\frac{371497865363828920513536644882370201854777132381455057788506308}{154581749510447292884833232354359878417836593493315729674605}\cdot t^{33}-\frac{512108254151135547852259558623146600023144727080480161825392156}{370059339737131398118237131999831224091184572302180080130115}\cdot t^{31}+\frac{1790823813057217637811544466987252550653376559559134886397736}{2716787143787616493415311536372509542827383956834692468141}\cdot t^{29}-\frac{24030238398977675410140547778034408042356873222477693971369736}{92617743538214198639158347830881007141842634892091788686625}\cdot t^{27}+\frac{2548547539941198206873918278013882317931039922634328918289168868}{30299723284186889502951321718154516151255407185253584054405875}\cdot t^{25}-\frac{49272856032172594542928456915136219813661861552322722966823172}{2206441387874122209958506504604072458193983497592825095243915}\cdot t^{23}+\frac{8693974690541318009081893048550250365799196779514168411465387}{1805270226442463626329687140130604738522350134394129623381385}\cdot t^{21}-\frac{87444186110735387422731393039229738654711341592734553908894139}{104826024482092387902210499936917115150197797803819126797679089}\cdot t^{19}+\frac{205021450572295218989161631170165472217759485459485176860815238}{1793076734562106635169390130499898022306014962433748221539247575}\cdot t^{17}-\frac{21805410775064497263505076440144131440319221254007919702772486}{1793076734562106635169390130499898022306014962433748221539247575}\cdot t^{15}+\frac{2220840470040586843748908815772733082464029099994301959636744}{2271230530445335071214560831966537494920952285749414413949713595}\cdot t^{13}-\frac{4749334942945288109966609337776615208758242154544819393272}{82757387749020306238587236792302985644892998266172994840272965}\cdot t^{11}+\frac{225105553675691833066784022233135027966043901742128219754186}{96144523727257281958672884896686979522758689276611924569253120811}\cdot t^9-\frac{11080127073698927567593474517830370089462347208330919348786198}{179202709502748989428526404904658231277141890290573892738802344622725}\cdot t^7+\frac{56436889156108781117292142314435168514749121310083556903677}{59734236500916329809508801634886077092380630096857964246267448207575}\cdot t^5-\frac{8089518484463856892709832714013988119266975342906963279203}{1182737882718143330228274272370744326429136475917787692076095474509985}\cdot t^3+\frac{5843346075187578768997559019453346440006139200337170784}{394245960906047776742758090790248108809712158639262564025365158169995}\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.